Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
4.1-a1 |
4.1-a |
$2$ |
$2$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{6} \) |
$10.63992$ |
$(-2a^3-3a^2+13a+14)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$597.5219103$ |
1.491941013 |
\( \frac{1089737}{16} a^{3} - \frac{2179965}{16} a^{2} - \frac{9824099}{16} a + \frac{10538913}{8} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( a + 1\) , \( a^{3} + 2 a^{2} - 7 a - 11\) , \( 3 a^{3} - 13 a^{2} + 19 a - 7\) , \( \frac{59}{2} a^{3} - \frac{241}{2} a^{2} + \frac{137}{2} a + 122\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){x}{y}+\left(a^{3}+2a^{2}-7a-11\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a^{3}-13a^{2}+19a-7\right){x}+\frac{59}{2}a^{3}-\frac{241}{2}a^{2}+\frac{137}{2}a+122$ |
4.1-a2 |
4.1-a |
$2$ |
$2$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{12} \) |
$10.63992$ |
$(-2a^3-3a^2+13a+14)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$298.7609551$ |
1.491941013 |
\( -\frac{74875}{128} a^{3} - \frac{81775}{128} a^{2} + \frac{619595}{128} a + \frac{34859}{8} \) |
\( \bigl[a + 1\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 8\) , \( a + 1\) , \( \frac{5}{2} a^{3} + \frac{7}{2} a^{2} - \frac{37}{2} a - 17\) , \( \frac{3}{2} a^{3} + \frac{5}{2} a^{2} - \frac{21}{2} a - 13\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{7}{2}a-8\right){x}^{2}+\left(\frac{5}{2}a^{3}+\frac{7}{2}a^{2}-\frac{37}{2}a-17\right){x}+\frac{3}{2}a^{3}+\frac{5}{2}a^{2}-\frac{21}{2}a-13$ |
4.2-a1 |
4.2-a |
$2$ |
$2$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{6} \) |
$10.63992$ |
$(-3/2a^3-3/2a^2+23/2a+8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$597.5219103$ |
1.491941013 |
\( 306020 a^{3} + \frac{4083011}{8} a^{2} - \frac{8019575}{4} a - \frac{4581829}{2} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 8\) , \( a^{2} - a - 6\) , \( a^{3} + 2 a^{2} - 7 a - 10\) , \( -\frac{97}{2} a^{3} - \frac{161}{2} a^{2} + \frac{619}{2} a + 352\) , \( -\frac{715}{2} a^{3} - \frac{1189}{2} a^{2} + \frac{4683}{2} a + 2675\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{7}{2}a-8\right){x}{y}+\left(a^{3}+2a^{2}-7a-10\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-\frac{97}{2}a^{3}-\frac{161}{2}a^{2}+\frac{619}{2}a+352\right){x}-\frac{715}{2}a^{3}-\frac{1189}{2}a^{2}+\frac{4683}{2}a+2675$ |
4.2-a2 |
4.2-a |
$2$ |
$2$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{12} \) |
$10.63992$ |
$(-3/2a^3-3/2a^2+23/2a+8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$298.7609551$ |
1.491941013 |
\( -\frac{8395}{64} a^{3} - \frac{4945}{64} a^{2} + \frac{5515}{32} a + \frac{29463}{16} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( a^{2} - 5\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( a^{2} - 3 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - 4\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(a^{2}-3a+1\right){x}-\frac{1}{2}a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}a-4$ |
5.1-a1 |
5.1-a |
$6$ |
$8$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$10.94087$ |
$(-a^3-a^2+8a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1449.651089$ |
1.809803020 |
\( -\frac{11193}{2} a^{3} + \frac{173187}{10} a^{2} + \frac{12873}{10} a - \frac{46001}{5} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 8\) , \( a^{2} + a - 6\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 8\) , \( 3 a - 5\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a^{2} + \frac{1}{2} a + 6\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{7}{2}a-8\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-8\right){y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(3a-5\right){x}+\frac{1}{2}a^{3}-\frac{5}{2}a^{2}+\frac{1}{2}a+6$ |
5.1-a2 |
5.1-a |
$6$ |
$8$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( -5 \) |
$10.94087$ |
$(-a^3-a^2+8a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$181.2063861$ |
1.809803020 |
\( -\frac{14850785337}{10} a^{3} + \frac{58141900917}{10} a^{2} - \frac{13838253573}{10} a - 9396223342 \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( -a^{3} - 2 a^{2} + 8 a + 11\) , \( a^{3} + 2 a^{2} - 7 a - 10\) , \( a^{3} - 5 a^{2} - 2 a + 35\) , \( 14 a^{3} - 25 a^{2} - 113 a + 230\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-7\right){x}{y}+\left(a^{3}+2a^{2}-7a-10\right){y}={x}^{3}+\left(-a^{3}-2a^{2}+8a+11\right){x}^{2}+\left(a^{3}-5a^{2}-2a+35\right){x}+14a^{3}-25a^{2}-113a+230$ |
5.1-a3 |
5.1-a |
$6$ |
$8$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{4} \) |
$10.94087$ |
$(-a^3-a^2+8a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1449.651089$ |
1.809803020 |
\( \frac{15523}{50} a^{3} + \frac{2093}{10} a^{2} - \frac{87361}{50} a + \frac{76896}{25} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 3\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{5}{2} a + 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 2\) , \( 8 a^{3} + 12 a^{2} - 61 a - 68\) , \( \frac{19}{2} a^{3} + \frac{27}{2} a^{2} - \frac{147}{2} a - 81\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{5}{2}a+2\right){x}^{2}+\left(8a^{3}+12a^{2}-61a-68\right){x}+\frac{19}{2}a^{3}+\frac{27}{2}a^{2}-\frac{147}{2}a-81$ |
5.1-a4 |
5.1-a |
$6$ |
$8$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{8} \) |
$10.94087$ |
$(-a^3-a^2+8a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$362.4127723$ |
1.809803020 |
\( \frac{6422485589}{1250} a^{3} + \frac{7774503269}{1250} a^{2} - \frac{44185663437}{1250} a - \frac{13690349419}{625} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 3\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{5}{2} a + 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 2\) , \( -17 a^{3} - 23 a^{2} + 129 a + 137\) , \( \frac{175}{2} a^{3} + \frac{247}{2} a^{2} - \frac{1333}{2} a - 730\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{5}{2}a+2\right){x}^{2}+\left(-17a^{3}-23a^{2}+129a+137\right){x}+\frac{175}{2}a^{3}+\frac{247}{2}a^{2}-\frac{1333}{2}a-730$ |
5.1-a5 |
5.1-a |
$6$ |
$8$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{2} \) |
$10.94087$ |
$(-a^3-a^2+8a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$362.4127723$ |
1.809803020 |
\( -\frac{5288913}{2} a^{3} - \frac{36986157}{10} a^{2} + \frac{202168277}{10} a + \frac{110247891}{5} \) |
\( \bigl[a + 1\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 7\) , \( a^{3} + 2 a^{2} - 7 a - 10\) , \( \frac{1}{2} a^{3} + \frac{5}{2} a^{2} - \frac{9}{2} a - 5\) , \( 2 a^{3} + 5 a^{2} - 15 a - 20\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+2a^{2}-7a-10\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{7}{2}a-7\right){x}^{2}+\left(\frac{1}{2}a^{3}+\frac{5}{2}a^{2}-\frac{9}{2}a-5\right){x}+2a^{3}+5a^{2}-15a-20$ |
5.1-a6 |
5.1-a |
$6$ |
$8$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( -5 \) |
$10.94087$ |
$(-a^3-a^2+8a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$724.8255447$ |
1.809803020 |
\( \frac{74930497}{10} a^{3} - \frac{152849237}{10} a^{2} - \frac{665288827}{10} a + 144112670 \) |
\( \bigl[a + 1\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{5}{2} a + 2\) , \( a + 1\) , \( \frac{5}{2} a^{3} + \frac{13}{2} a^{2} - \frac{19}{2} a - 14\) , \( -247 a^{3} - 378 a^{2} + 1755 a + 1956\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{5}{2}a+2\right){x}^{2}+\left(\frac{5}{2}a^{3}+\frac{13}{2}a^{2}-\frac{19}{2}a-14\right){x}-247a^{3}-378a^{2}+1755a+1956$ |
5.2-a1 |
5.2-a |
$6$ |
$8$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( -5 \) |
$10.94087$ |
$(a^3+2a^2-7a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$181.2063861$ |
1.809803020 |
\( -\frac{91618345092}{5} a^{3} - \frac{128114688219}{5} a^{2} + 140045058222 a + 152848630727 \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 8\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 4\) , \( a^{3} + 2 a^{2} - 7 a - 11\) , \( \frac{31}{2} a^{3} + \frac{51}{2} a^{2} - \frac{221}{2} a - 130\) , \( \frac{175}{2} a^{3} + \frac{281}{2} a^{2} - \frac{1191}{2} a - 678\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-8\right){x}{y}+\left(a^{3}+2a^{2}-7a-11\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-4\right){x}^{2}+\left(\frac{31}{2}a^{3}+\frac{51}{2}a^{2}-\frac{221}{2}a-130\right){x}+\frac{175}{2}a^{3}+\frac{281}{2}a^{2}-\frac{1191}{2}a-678$ |
5.2-a2 |
5.2-a |
$6$ |
$8$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( 5^{2} \) |
$10.94087$ |
$(a^3+2a^2-7a-9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1449.651089$ |
1.809803020 |
\( -\frac{294567}{5} a^{3} - \frac{409143}{5} a^{2} + 450282 a + 501965 \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 8\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 4\) , \( a^{3} + 2 a^{2} - 7 a - 11\) , \( -2 a^{3} - 2 a^{2} + 12 a + 10\) , \( -\frac{1}{2} a^{3} - \frac{3}{2} a^{2} + \frac{7}{2} a + 4\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-8\right){x}{y}+\left(a^{3}+2a^{2}-7a-11\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-4\right){x}^{2}+\left(-2a^{3}-2a^{2}+12a+10\right){x}-\frac{1}{2}a^{3}-\frac{3}{2}a^{2}+\frac{7}{2}a+4$ |
5.2-a3 |
5.2-a |
$6$ |
$8$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( -5 \) |
$10.94087$ |
$(a^3+2a^2-7a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$724.8255447$ |
1.809803020 |
\( \frac{173106212}{5} a^{3} + \frac{286996079}{5} a^{2} - 228271162 a - 260513755 \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 8\) , \( -a^{3} - 2 a^{2} + 8 a + 11\) , \( a^{3} + 2 a^{2} - 7 a - 11\) , \( -\frac{11}{2} a^{3} + \frac{31}{2} a^{2} + \frac{3}{2} a - 5\) , \( -\frac{325}{2} a^{3} + \frac{1309}{2} a^{2} - \frac{359}{2} a - 1088\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-8\right){x}{y}+\left(a^{3}+2a^{2}-7a-11\right){y}={x}^{3}+\left(-a^{3}-2a^{2}+8a+11\right){x}^{2}+\left(-\frac{11}{2}a^{3}+\frac{31}{2}a^{2}+\frac{3}{2}a-5\right){x}-\frac{325}{2}a^{3}+\frac{1309}{2}a^{2}-\frac{359}{2}a-1088$ |
5.2-a4 |
5.2-a |
$6$ |
$8$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{8} \) |
$10.94087$ |
$(a^3+2a^2-7a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$362.4127723$ |
1.809803020 |
\( \frac{2390163456}{625} a^{3} + \frac{1714154616}{625} a^{2} - \frac{3423402407}{125} a - \frac{323583429}{125} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 3\) , \( -a^{3} + 7 a^{2} - 3 a - 19\) , \( \frac{15}{2} a^{3} - \frac{63}{2} a^{2} + \frac{17}{2} a + 57\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){x}^{2}+\left(-a^{3}+7a^{2}-3a-19\right){x}+\frac{15}{2}a^{3}-\frac{63}{2}a^{2}+\frac{17}{2}a+57$ |
5.2-a5 |
5.2-a |
$6$ |
$8$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( 5^{4} \) |
$10.94087$ |
$(a^3+2a^2-7a-9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1449.651089$ |
1.809803020 |
\( \frac{3376}{5} a^{3} + \frac{19409}{25} a^{2} - \frac{25762}{5} a + \frac{1509}{5} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 3\) , \( \frac{3}{2} a^{3} - \frac{1}{2} a^{2} - \frac{11}{2} a - 4\) , \( a^{3} - a^{2} - 3 a - 1\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){x}^{2}+\left(\frac{3}{2}a^{3}-\frac{1}{2}a^{2}-\frac{11}{2}a-4\right){x}+a^{3}-a^{2}-3a-1$ |
5.2-a6 |
5.2-a |
$6$ |
$8$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{2} \) |
$10.94087$ |
$(a^3+2a^2-7a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$362.4127723$ |
1.809803020 |
\( -\frac{1052008}{5} a^{3} + \frac{4218788}{5} a^{2} - 232821 a - 1390711 \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( a^{2} - 4\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 8\) , \( -\frac{3}{2} a^{3} + \frac{3}{2} a^{2} + \frac{13}{2} a + 7\) , \( -a^{3} + 3 a^{2} + 3 a - 5\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{7}{2}a-8\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-\frac{3}{2}a^{3}+\frac{3}{2}a^{2}+\frac{13}{2}a+7\right){x}-a^{3}+3a^{2}+3a-5$ |
16.1-a1 |
16.1-a |
$2$ |
$5$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$12.65307$ |
$(-2a^3-3a^2+13a+14), (-3/2a^3-3/2a^2+23/2a+8)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$712.4183883$ |
1.138447250 |
\( \frac{755}{8} a^{3} + \frac{755}{8} a^{2} - \frac{5285}{8} a - \frac{1419}{4} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 8\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 9\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( \frac{9}{2} a^{3} + \frac{17}{2} a^{2} - \frac{59}{2} a - 42\) , \( \frac{5}{2} a^{3} + \frac{9}{2} a^{2} - \frac{33}{2} a - 22\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-8\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-7\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{7}{2}a-9\right){x}^{2}+\left(\frac{9}{2}a^{3}+\frac{17}{2}a^{2}-\frac{59}{2}a-42\right){x}+\frac{5}{2}a^{3}+\frac{9}{2}a^{2}-\frac{33}{2}a-22$ |
16.1-a2 |
16.1-a |
$2$ |
$5$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{40} \) |
$12.65307$ |
$(-2a^3-3a^2+13a+14), (-3/2a^3-3/2a^2+23/2a+8)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.4[2] |
$25$ |
\( 2^{2} \) |
$1$ |
$1.139869421$ |
1.138447250 |
\( -\frac{1138132817779}{2048} a^{3} - \frac{1138132817779}{2048} a^{2} + \frac{7966929724453}{2048} a + \frac{393214741029}{256} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( a^{2} - a - 6\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( -\frac{409}{2} a^{3} + \frac{863}{2} a^{2} + \frac{3649}{2} a - 4045\) , \( -5735 a^{3} + 11714 a^{2} + 50945 a - 110458\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-7\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-\frac{409}{2}a^{3}+\frac{863}{2}a^{2}+\frac{3649}{2}a-4045\right){x}-5735a^{3}+11714a^{2}+50945a-110458$ |
16.1-b1 |
16.1-b |
$4$ |
$10$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{22} \) |
$12.65307$ |
$(-2a^3-3a^2+13a+14), (-3/2a^3-3/2a^2+23/2a+8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$509.7839379$ |
2.545739501 |
\( -\frac{156287283315}{1024} a^{3} + \frac{627810850135}{1024} a^{2} - \frac{87427248925}{512} a - \frac{258959821057}{256} \) |
\( \bigl[a^{3} + 2 a^{2} - 7 a - 11\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{7}{2} a + 3\) , \( a^{3} + 2 a^{2} - 7 a - 11\) , \( -126 a^{3} - 198 a^{2} + 873 a + 977\) , \( -\frac{155}{2} a^{3} - \frac{453}{2} a^{2} + \frac{225}{2} a + 273\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-7a-11\right){x}{y}+\left(a^{3}+2a^{2}-7a-11\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{7}{2}a+3\right){x}^{2}+\left(-126a^{3}-198a^{2}+873a+977\right){x}-\frac{155}{2}a^{3}-\frac{453}{2}a^{2}+\frac{225}{2}a+273$ |
16.1-b2 |
16.1-b |
$4$ |
$10$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{22} \) |
$12.65307$ |
$(-2a^3-3a^2+13a+14), (-3/2a^3-3/2a^2+23/2a+8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$509.7839379$ |
2.545739501 |
\( -\frac{3933734448035}{2048} a^{3} - \frac{5501930714935}{2048} a^{2} + \frac{30073872098355}{2048} a + \frac{2049969526679}{128} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 8\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{7}{2} a + 3\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 8\) , \( -\frac{45}{2} a^{3} + \frac{99}{2} a^{2} + \frac{333}{2} a - 373\) , \( -69 a^{3} + 80 a^{2} + 913 a - 1698\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{7}{2}a-8\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{7}{2}a-8\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{7}{2}a+3\right){x}^{2}+\left(-\frac{45}{2}a^{3}+\frac{99}{2}a^{2}+\frac{333}{2}a-373\right){x}-69a^{3}+80a^{2}+913a-1698$ |
16.1-b3 |
16.1-b |
$4$ |
$10$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{14} \) |
$12.65307$ |
$(-2a^3-3a^2+13a+14), (-3/2a^3-3/2a^2+23/2a+8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$509.7839379$ |
2.545739501 |
\( 14738059585 a^{3} - \frac{961987350305}{32} a^{2} - \frac{2093670760475}{16} a + \frac{2267536003599}{8} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 8\) , \( a\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( -\frac{37}{2} a^{3} + \frac{91}{2} a^{2} + \frac{361}{2} a - 439\) , \( 173 a^{3} - 327 a^{2} - 1569 a + 3256\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-8\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-7\right){y}={x}^{3}+a{x}^{2}+\left(-\frac{37}{2}a^{3}+\frac{91}{2}a^{2}+\frac{361}{2}a-439\right){x}+173a^{3}-327a^{2}-1569a+3256$ |
16.1-b4 |
16.1-b |
$4$ |
$10$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{14} \) |
$12.65307$ |
$(-2a^3-3a^2+13a+14), (-3/2a^3-3/2a^2+23/2a+8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$509.7839379$ |
2.545739501 |
\( \frac{4358035410605}{64} a^{3} + \frac{7225245924655}{64} a^{2} - \frac{28734215526415}{64} a - \frac{16396323521259}{32} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( -a^{2} + a + 6\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( -83 a^{3} - 142 a^{2} + 531 a + 628\) , \( \frac{1029}{2} a^{3} + \frac{1713}{2} a^{2} - \frac{6735}{2} a - 3839\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-7\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-83a^{3}-142a^{2}+531a+628\right){x}+\frac{1029}{2}a^{3}+\frac{1713}{2}a^{2}-\frac{6735}{2}a-3839$ |
19.1-a1 |
19.1-a |
$4$ |
$4$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( -19 \) |
$12.92781$ |
$(-1/2a^3-1/2a^2+9/2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.856616323$ |
$333.7677003$ |
2.855541403 |
\( -\frac{496999345}{38} a^{3} + \frac{2021811873}{38} a^{2} - \frac{685587759}{38} a - \frac{1564393896}{19} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 8\) , \( 0\) , \( a + 1\) , \( 5 a^{3} - 10 a^{2} - 10 a + 10\) , \( \frac{37}{2} a^{3} - \frac{125}{2} a^{2} + \frac{7}{2} a + 93\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-8\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(5a^{3}-10a^{2}-10a+10\right){x}+\frac{37}{2}a^{3}-\frac{125}{2}a^{2}+\frac{7}{2}a+93$ |
19.1-a2 |
19.1-a |
$4$ |
$4$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$12.92781$ |
$(-1/2a^3-1/2a^2+9/2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.713232646$ |
$333.7677003$ |
2.855541403 |
\( -\frac{10122778285}{722} a^{3} - \frac{14147952395}{722} a^{2} + \frac{77422321485}{722} a + \frac{42214565763}{361} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( -a^{2} + 5\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( -\frac{19}{2} a^{3} - \frac{37}{2} a^{2} + \frac{113}{2} a + 84\) , \( -84 a^{3} - 143 a^{2} + 547 a + 640\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-7\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-\frac{19}{2}a^{3}-\frac{37}{2}a^{2}+\frac{113}{2}a+84\right){x}-84a^{3}-143a^{2}+547a+640$ |
19.1-a3 |
19.1-a |
$4$ |
$4$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{4} \) |
$12.92781$ |
$(-1/2a^3-1/2a^2+9/2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.856616323$ |
$83.44192508$ |
2.855541403 |
\( -\frac{249011005281093872105}{260642} a^{3} - \frac{348283791479947969831}{260642} a^{2} + \frac{1903703779195375836781}{260642} a + \frac{1038121897048822698256}{130321} \) |
\( \bigl[a + 1\) , \( 0\) , \( a^{3} + 2 a^{2} - 7 a - 11\) , \( -148 a^{3} - 247 a^{2} + 969 a + 1109\) , \( -\frac{187}{2} a^{3} - \frac{323}{2} a^{2} + \frac{1179}{2} a + 681\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+2a^{2}-7a-11\right){y}={x}^{3}+\left(-148a^{3}-247a^{2}+969a+1109\right){x}-\frac{187}{2}a^{3}-\frac{323}{2}a^{2}+\frac{1179}{2}a+681$ |
19.1-a4 |
19.1-a |
$4$ |
$4$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19 \) |
$12.92781$ |
$(-1/2a^3-1/2a^2+9/2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$3.426465292$ |
$83.44192508$ |
2.855541403 |
\( \frac{469006507195}{38} a^{3} + \frac{777574910221}{38} a^{2} - \frac{3092339842255}{38} a - \frac{1764562101548}{19} \) |
\( \bigl[a + 1\) , \( -a^{3} - 2 a^{2} + 7 a + 11\) , \( a + 1\) , \( -7 a^{3} + 11 a^{2} + 38 a - 54\) , \( \frac{273}{2} a^{3} - \frac{1159}{2} a^{2} + \frac{573}{2} a + 766\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}-2a^{2}+7a+11\right){x}^{2}+\left(-7a^{3}+11a^{2}+38a-54\right){x}+\frac{273}{2}a^{3}-\frac{1159}{2}a^{2}+\frac{573}{2}a+766$ |
19.2-a1 |
19.2-a |
$4$ |
$4$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{4} \) |
$12.92781$ |
$(a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.856616323$ |
$83.44192508$ |
2.855541403 |
\( -\frac{19788454868953359493}{260642} a^{3} + \frac{4183385859468459907}{13718} a^{2} - \frac{22107558145045215595}{260642} a - \frac{65596314068009962187}{130321} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 8\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{5}{2} a + 4\) , \( a^{3} + 2 a^{2} - 6 a - 11\) , \( -2 a^{3} - 9 a^{2} + 55 a - 53\) , \( 24 a^{3} - 119 a^{2} + 124 a + 56\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-8\right){x}{y}+\left(a^{3}+2a^{2}-6a-11\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{5}{2}a+4\right){x}^{2}+\left(-2a^{3}-9a^{2}+55a-53\right){x}+24a^{3}-119a^{2}+124a+56$ |
19.2-a2 |
19.2-a |
$4$ |
$4$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{2} \) |
$12.92781$ |
$(a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.713232646$ |
$333.7677003$ |
2.855541403 |
\( -\frac{803580375}{722} a^{3} + \frac{169557565}{38} a^{2} - \frac{937810865}{722} a - \frac{2587461772}{361} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 8\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{5}{2} a + 4\) , \( a^{3} + 2 a^{2} - 6 a - 11\) , \( -\frac{9}{2} a^{3} + \frac{7}{2} a^{2} + \frac{75}{2} a - 48\) , \( -18 a^{3} + 32 a^{2} + 166 a - 334\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-8\right){x}{y}+\left(a^{3}+2a^{2}-6a-11\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{5}{2}a+4\right){x}^{2}+\left(-\frac{9}{2}a^{3}+\frac{7}{2}a^{2}+\frac{75}{2}a-48\right){x}-18a^{3}+32a^{2}+166a-334$ |
19.2-a3 |
19.2-a |
$4$ |
$4$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( -19 \) |
$12.92781$ |
$(a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.856616323$ |
$333.7677003$ |
2.855541403 |
\( -\frac{6357507759}{38} a^{3} - \frac{467174683}{2} a^{2} + \frac{48667137487}{38} a + \frac{26528895849}{19} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( -\frac{1}{2} a^{3} - \frac{3}{2} a^{2} + \frac{5}{2} a + 8\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( \frac{77}{2} a^{3} + \frac{103}{2} a^{2} - \frac{593}{2} a - 305\) , \( 206 a^{3} + 286 a^{2} - 1575 a - 1704\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-7\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{3}{2}a^{2}+\frac{5}{2}a+8\right){x}^{2}+\left(\frac{77}{2}a^{3}+\frac{103}{2}a^{2}-\frac{593}{2}a-305\right){x}+206a^{3}+286a^{2}-1575a-1704$ |
19.2-a4 |
19.2-a |
$4$ |
$4$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19 \) |
$12.92781$ |
$(a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$3.426465292$ |
$83.44192508$ |
2.855541403 |
\( \frac{101506756711}{38} a^{3} - \frac{10897981385}{2} a^{2} - \frac{901253005087}{38} a + \frac{976132019089}{19} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( 0\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( -\frac{81}{2} a^{3} - \frac{121}{2} a^{2} + \frac{589}{2} a + 326\) , \( 1831 a^{3} + 2546 a^{2} - 14059 a - 15314\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){y}={x}^{3}+\left(-\frac{81}{2}a^{3}-\frac{121}{2}a^{2}+\frac{589}{2}a+326\right){x}+1831a^{3}+2546a^{2}-14059a-15314$ |
20.1-a1 |
20.1-a |
$2$ |
$2$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{4} \cdot 5^{8} \) |
$13.01096$ |
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.015784360$ |
$767.7566759$ |
1.936548564 |
\( -\frac{3863203}{5000} a^{3} - \frac{1529269}{5000} a^{2} + \frac{5761753}{1000} a + \frac{897131}{2500} \) |
\( \bigl[a^{3} + 2 a^{2} - 7 a - 11\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 9\) , \( 0\) , \( \frac{3}{2} a^{3} + \frac{5}{2} a^{2} - \frac{21}{2} a - 12\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 1\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-7a-11\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{7}{2}a-9\right){x}^{2}+\left(\frac{3}{2}a^{3}+\frac{5}{2}a^{2}-\frac{21}{2}a-12\right){x}+\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-1$ |
20.1-a2 |
20.1-a |
$2$ |
$2$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{2} \cdot 5^{4} \) |
$13.01096$ |
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.031568721$ |
$1535.513351$ |
1.936548564 |
\( \frac{182677883}{100} a^{3} - \frac{192924401}{100} a^{2} - \frac{302177551}{20} a + \frac{553290657}{25} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 2\) , \( -a^{3} - 2 a^{2} + 8 a + 11\) , \( 0\) , \( \frac{7}{2} a^{3} - \frac{51}{2} a^{2} + \frac{59}{2} a + 36\) , \( -28 a^{3} + 110 a^{2} - 37 a - 153\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-2\right){x}{y}={x}^{3}+\left(-a^{3}-2a^{2}+8a+11\right){x}^{2}+\left(\frac{7}{2}a^{3}-\frac{51}{2}a^{2}+\frac{59}{2}a+36\right){x}-28a^{3}+110a^{2}-37a-153$ |
20.1-b1 |
20.1-b |
$2$ |
$5$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{6} \cdot 5 \) |
$13.01096$ |
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 3 \) |
$0.143889975$ |
$158.3651871$ |
2.731047863 |
\( \frac{28070492964911}{80} a^{3} + \frac{46534585073479}{80} a^{2} - \frac{185095906131291}{80} a - \frac{10561713398469}{4} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 7\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{9}{2} a - 7\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 8\) , \( 375 a^{3} + 570 a^{2} - 2855 a - 3479\) , \( -\frac{13691}{2} a^{3} - \frac{18561}{2} a^{2} + \frac{104869}{2} a + 54734\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{7}{2}a-7\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{7}{2}a-8\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{9}{2}a-7\right){x}^{2}+\left(375a^{3}+570a^{2}-2855a-3479\right){x}-\frac{13691}{2}a^{3}-\frac{18561}{2}a^{2}+\frac{104869}{2}a+54734$ |
20.1-b2 |
20.1-b |
$2$ |
$5$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{30} \cdot 5^{5} \) |
$13.01096$ |
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 3 \cdot 5 \) |
$0.028777995$ |
$158.3651871$ |
2.731047863 |
\( \frac{2515245321}{8192000} a^{3} + \frac{3001005979}{8192000} a^{2} - \frac{16475442011}{8192000} a - \frac{807504311}{819200} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 7\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 8\) , \( 13 a^{3} - 11 a^{2} - 100 a + 126\) , \( \frac{43}{2} a^{3} - \frac{3}{2} a^{2} - \frac{565}{2} a + 390\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{7}{2}a-7\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{7}{2}a-8\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-7\right){x}^{2}+\left(13a^{3}-11a^{2}-100a+126\right){x}+\frac{43}{2}a^{3}-\frac{3}{2}a^{2}-\frac{565}{2}a+390$ |
20.1-c1 |
20.1-c |
$6$ |
$8$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5^{8} \) |
$13.01096$ |
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$430.0040155$ |
2.147337581 |
\( -\frac{113548311}{1250} a^{3} + \frac{213059727}{625} a^{2} + \frac{2745414}{625} a - \frac{890928423}{1250} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 8\) , \( a + 1\) , \( a^{3} + 2 a^{2} - 6 a - 11\) , \( \frac{11}{2} a^{3} - \frac{25}{2} a^{2} - \frac{9}{2} a + 11\) , \( \frac{55}{2} a^{3} - \frac{173}{2} a^{2} - \frac{1}{2} a + 121\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{7}{2}a-8\right){x}{y}+\left(a^{3}+2a^{2}-6a-11\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(\frac{11}{2}a^{3}-\frac{25}{2}a^{2}-\frac{9}{2}a+11\right){x}+\frac{55}{2}a^{3}-\frac{173}{2}a^{2}-\frac{1}{2}a+121$ |
20.1-c2 |
20.1-c |
$6$ |
$8$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \) |
$13.01096$ |
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$860.0080310$ |
2.147337581 |
\( \frac{243261627651}{100} a^{3} - \frac{49622658939}{10} a^{2} - \frac{539965019853}{25} a + \frac{4678629211449}{100} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 4\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( -\frac{99}{2} a^{3} - \frac{165}{2} a^{2} + \frac{649}{2} a + 372\) , \( 114 a^{3} + 189 a^{2} - 753 a - 862\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-7\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-4\right){x}^{2}+\left(-\frac{99}{2}a^{3}-\frac{165}{2}a^{2}+\frac{649}{2}a+372\right){x}+114a^{3}+189a^{2}-753a-862$ |
20.1-c3 |
20.1-c |
$6$ |
$8$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{16} \cdot 5 \) |
$13.01096$ |
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$430.0040155$ |
2.147337581 |
\( -\frac{17026072749}{1280} a^{3} + \frac{34201642257}{640} a^{2} - \frac{4761303849}{320} a - \frac{22583866095}{256} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( -a + 1\) , \( 1\) , \( -a^{3} + 4 a + 4\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{9}{2} a - 5\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a^{3}+4a+4\right){x}+\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{9}{2}a-5$ |
20.1-c4 |
20.1-c |
$6$ |
$8$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5^{2} \) |
$13.01096$ |
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$107.5010038$ |
2.147337581 |
\( \frac{297484419302612140095}{2} a^{3} - \frac{1517085400821149859651}{5} a^{2} - \frac{6603226384970789684334}{5} a + \frac{28607420014105624581267}{10} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 2\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{7}{2} a + 4\) , \( a^{3} + 2 a^{2} - 6 a - 10\) , \( -\frac{167}{2} a^{3} - \frac{267}{2} a^{2} + \frac{1133}{2} a + 642\) , \( -300 a^{3} - 549 a^{2} + 1768 a + 2093\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-2\right){x}{y}+\left(a^{3}+2a^{2}-6a-10\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{7}{2}a+4\right){x}^{2}+\left(-\frac{167}{2}a^{3}-\frac{267}{2}a^{2}+\frac{1133}{2}a+642\right){x}-300a^{3}-549a^{2}+1768a+2093$ |
20.1-c5 |
20.1-c |
$6$ |
$8$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{4} \cdot 5 \) |
$13.01096$ |
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$107.5010038$ |
2.147337581 |
\( -\frac{67604167077396039}{20} a^{3} - \frac{47277455659500033}{10} a^{2} + \frac{129210362820033741}{5} a + \frac{112736727397831167}{4} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 2\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{7}{2} a + 4\) , \( 0\) , \( -12 a^{3} + 21 a^{2} + 73 a - 128\) , \( -238 a^{3} + 959 a^{2} - 242 a - 1652\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-2\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{7}{2}a+4\right){x}^{2}+\left(-12a^{3}+21a^{2}+73a-128\right){x}-238a^{3}+959a^{2}-242a-1652$ |
20.1-c6 |
20.1-c |
$6$ |
$8$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$13.01096$ |
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$860.0080310$ |
2.147337581 |
\( -\frac{420394617}{16} a^{3} - \frac{1469389167}{40} a^{2} + \frac{4020842511}{20} a + \frac{17558935029}{80} \) |
\( \bigl[1\) , \( -1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 2\) , \( \frac{109}{2} a^{3} - \frac{443}{2} a^{2} + \frac{139}{2} a + 356\) , \( -1213 a^{3} + 4874 a^{2} - 1366 a - 8026\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-2\right){y}={x}^{3}-{x}^{2}+\left(\frac{109}{2}a^{3}-\frac{443}{2}a^{2}+\frac{139}{2}a+356\right){x}-1213a^{3}+4874a^{2}-1366a-8026$ |
20.1-d1 |
20.1-d |
$4$ |
$4$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5^{4} \) |
$13.01096$ |
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$241.8213273$ |
1.207598081 |
\( -\frac{115959}{4} a^{3} + \frac{2789331}{100} a^{2} + \frac{10742409}{100} a + \frac{2469607}{50} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 8\) , \( a^{2} - 5\) , \( a^{3} + 2 a^{2} - 7 a - 10\) , \( 14 a^{3} - 41 a^{2} - 4 a + 54\) , \( 137 a^{3} - 525 a^{2} + 119 a + 844\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-8\right){x}{y}+\left(a^{3}+2a^{2}-7a-10\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(14a^{3}-41a^{2}-4a+54\right){x}+137a^{3}-525a^{2}+119a+844$ |
20.1-d2 |
20.1-d |
$4$ |
$4$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{2} \) |
$13.01096$ |
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$483.6426547$ |
1.207598081 |
\( \frac{1261573141}{40} a^{3} + \frac{2091566977}{40} a^{2} - \frac{8318045629}{40} a - \frac{1186589156}{5} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{9}{2} a + 4\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( 3 a^{3} + 6 a^{2} - 17 a - 25\) , \( \frac{7}{2} a^{3} + \frac{13}{2} a^{2} - \frac{43}{2} a - 28\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-7\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-7\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{9}{2}a+4\right){x}^{2}+\left(3a^{3}+6a^{2}-17a-25\right){x}+\frac{7}{2}a^{3}+\frac{13}{2}a^{2}-\frac{43}{2}a-28$ |
20.1-d3 |
20.1-d |
$4$ |
$4$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5 \) |
$13.01096$ |
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$120.9106636$ |
1.207598081 |
\( \frac{108228121969295379}{20} a^{3} + \frac{179433515162009521}{20} a^{2} - \frac{713589500604580069}{20} a - \frac{81438223753542063}{2} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{9}{2} a + 4\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( -17 a^{3} - 29 a^{2} + 113 a + 125\) , \( -\frac{393}{2} a^{3} - \frac{653}{2} a^{2} + \frac{2563}{2} a + 1462\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-7\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-7\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{9}{2}a+4\right){x}^{2}+\left(-17a^{3}-29a^{2}+113a+125\right){x}-\frac{393}{2}a^{3}-\frac{653}{2}a^{2}+\frac{2563}{2}a+1462$ |
20.1-d4 |
20.1-d |
$4$ |
$4$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5 \) |
$13.01096$ |
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$241.8213273$ |
1.207598081 |
\( \frac{131631773}{160} a^{3} - \frac{267156093}{160} a^{2} - \frac{1167892923}{160} a + \frac{252207087}{16} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{9}{2} a - 2\) , \( a^{3} + 2 a^{2} - 7 a - 10\) , \( -46 a^{3} - 67 a^{2} + 342 a + 380\) , \( 108 a^{3} + 146 a^{2} - 846 a - 916\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}+2a^{2}-7a-10\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{9}{2}a-2\right){x}^{2}+\left(-46a^{3}-67a^{2}+342a+380\right){x}+108a^{3}+146a^{2}-846a-916$ |
20.1-e1 |
20.1-e |
$2$ |
$2$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5^{2} \) |
$13.01096$ |
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$354.0558176$ |
1.768070379 |
\( -\frac{201169}{10} a^{3} - \frac{137492}{5} a^{2} + \frac{761396}{5} a + \frac{1670253}{10} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{5}{2} a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{19}{2} a^{2} + \frac{21}{2} a + 22\) , \( 15 a^{3} - 65 a^{2} + 23 a + 111\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{5}{2}a+3\right){x}^{2}+\left(\frac{1}{2}a^{3}-\frac{19}{2}a^{2}+\frac{21}{2}a+22\right){x}+15a^{3}-65a^{2}+23a+111$ |
20.1-e2 |
20.1-e |
$2$ |
$2$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5 \) |
$13.01096$ |
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$354.0558176$ |
1.768070379 |
\( \frac{2030751}{20} a^{3} + \frac{1680747}{10} a^{2} - \frac{3348359}{5} a - \frac{3048159}{4} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 2\) , \( a^{3} + 2 a^{2} - 7 a - 11\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{11}{2} a - 19\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 2\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-2\right){y}={x}^{3}+\left(a^{3}+2a^{2}-7a-11\right){x}^{2}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{11}{2}a-19\right){x}+\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-2$ |
20.1-f1 |
20.1-f |
$1$ |
$1$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{2} \cdot 5 \) |
$13.01096$ |
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.061346900$ |
$889.3328413$ |
2.179589741 |
\( \frac{70419}{20} a^{3} + \frac{175051}{20} a^{2} - \frac{486159}{20} a - 57297 \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 7\) , \( -a^{2} + a + 5\) , \( 1\) , \( 3 a^{3} - 9 a^{2} - 2 a + 16\) , \( -\frac{43}{2} a^{3} + \frac{177}{2} a^{2} - \frac{53}{2} a - 149\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{7}{2}a-7\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(3a^{3}-9a^{2}-2a+16\right){x}-\frac{43}{2}a^{3}+\frac{177}{2}a^{2}-\frac{53}{2}a-149$ |
20.1-g1 |
20.1-g |
$2$ |
$5$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{2} \cdot 5^{5} \) |
$13.01096$ |
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$93.21120410$ |
0.930949081 |
\( \frac{2872453914}{125} a^{3} + \frac{9523906047}{250} a^{2} - \frac{37881053973}{250} a - \frac{8646056991}{50} \) |
\( \bigl[a^{3} + 2 a^{2} - 6 a - 11\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{9}{2} a - 3\) , \( 1\) , \( 3 a^{3} - a^{2} - 24 a + 27\) , \( \frac{7}{2} a^{3} + \frac{5}{2} a^{2} - \frac{55}{2} a + 1\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-6a-11\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{9}{2}a-3\right){x}^{2}+\left(3a^{3}-a^{2}-24a+27\right){x}+\frac{7}{2}a^{3}+\frac{5}{2}a^{2}-\frac{55}{2}a+1$ |
20.1-g2 |
20.1-g |
$2$ |
$5$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{10} \cdot 5 \) |
$13.01096$ |
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$93.21120410$ |
0.930949081 |
\( -\frac{70032843}{40} a^{3} + \frac{575110287}{160} a^{2} + \frac{2493473787}{160} a - \frac{1084771791}{32} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 3\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 8\) , \( \frac{3}{2} a^{3} - \frac{81}{2} a^{2} + \frac{97}{2} a + 97\) , \( 72 a^{3} - 267 a^{2} + 51 a + 420\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{7}{2}a-8\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-3\right){x}^{2}+\left(\frac{3}{2}a^{3}-\frac{81}{2}a^{2}+\frac{97}{2}a+97\right){x}+72a^{3}-267a^{2}+51a+420$ |
20.2-a1 |
20.2-a |
$2$ |
$5$ |
4.4.10025.1 |
$4$ |
$[4, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5^{5} \) |
$13.01096$ |
$(-a^3-a^2+8a+5), (-3/2a^3-3/2a^2+23/2a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$0.170521335$ |
$417.9503753$ |
2.847221442 |
\( -\frac{242477}{125} a^{3} - \frac{213271}{250} a^{2} + \frac{1802457}{125} a - \frac{52346}{25} \) |
\( \bigl[a^{3} + 2 a^{2} - 7 a - 10\) , \( a^{3} + 2 a^{2} - 8 a - 12\) , \( a + 1\) , \( -\frac{67}{2} a^{3} - \frac{105}{2} a^{2} + \frac{461}{2} a + 260\) , \( -\frac{223}{2} a^{3} - \frac{387}{2} a^{2} + \frac{1399}{2} a + 811\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-7a-10\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}+2a^{2}-8a-12\right){x}^{2}+\left(-\frac{67}{2}a^{3}-\frac{105}{2}a^{2}+\frac{461}{2}a+260\right){x}-\frac{223}{2}a^{3}-\frac{387}{2}a^{2}+\frac{1399}{2}a+811$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.