| 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 |
| 1.1-a1 |
1.1-a |
$6$ |
$8$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.21575$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-32$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$644.1430735$ |
1.177988192 |
\( -\frac{18473000}{3} a^{3} + \frac{18473000}{3} a^{2} + 36946000 a + \frac{41429000}{3} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 3 a - \frac{14}{3}\) , \( -a^{2} + 5\) , \( a + 1\) , \( \frac{50}{3} a^{3} - \frac{119}{3} a^{2} - 67 a + \frac{301}{3}\) , \( 87 a^{3} - 211 a^{2} - 343 a + 493\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+3a-\frac{14}{3}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(\frac{50}{3}a^{3}-\frac{119}{3}a^{2}-67a+\frac{301}{3}\right){x}+87a^{3}-211a^{2}-343a+493$ |
| 1.1-a2 |
1.1-a |
$6$ |
$8$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.21575$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-32$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$644.1430735$ |
1.177988192 |
\( \frac{18473000}{3} a^{3} - \frac{18473000}{3} a^{2} - 36946000 a + \frac{115321000}{3} \) |
\( \bigl[a\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 3 a - \frac{20}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{17}{3}\) , \( -\frac{4}{3} a^{3} + \frac{13}{3} a^{2} + 6 a - \frac{20}{3}\) , \( 7 a^{3} - 16 a^{2} - 28 a + 37\bigr] \) |
${y}^2+a{x}{y}+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{17}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+3a-\frac{20}{3}\right){x}^{2}+\left(-\frac{4}{3}a^{3}+\frac{13}{3}a^{2}+6a-\frac{20}{3}\right){x}+7a^{3}-16a^{2}-28a+37$ |
| 1.1-a3 |
1.1-a |
$6$ |
$8$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.21575$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-32$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$644.1430735$ |
1.177988192 |
\( -\frac{18473000}{3} a^{3} + \frac{18473000}{3} a^{2} + 36946000 a + \frac{41429000}{3} \) |
\( \bigl[a\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 3 a + \frac{2}{3}\) , \( a^{2} + a - 5\) , \( \frac{46}{3} a^{3} - \frac{118}{3} a^{2} - 61 a + \frac{278}{3}\) , \( -\frac{230}{3} a^{3} + \frac{563}{3} a^{2} + 300 a - \frac{1306}{3}\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-3a+\frac{2}{3}\right){x}^{2}+\left(\frac{46}{3}a^{3}-\frac{118}{3}a^{2}-61a+\frac{278}{3}\right){x}-\frac{230}{3}a^{3}+\frac{563}{3}a^{2}+300a-\frac{1306}{3}$ |
| 1.1-a4 |
1.1-a |
$6$ |
$8$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.21575$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$2576.572294$ |
1.177988192 |
\( 8000 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + \frac{2}{3}\) , \( -\frac{2}{3} a^{3} + \frac{5}{3} a^{2} + 5 a - \frac{16}{3}\) , \( a^{2} - 5\) , \( -\frac{31}{3} a^{3} + \frac{58}{3} a^{2} + 73 a - \frac{266}{3}\) , \( \frac{182}{3} a^{3} - \frac{311}{3} a^{2} - 426 a + \frac{1462}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+\frac{2}{3}\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-\frac{2}{3}a^{3}+\frac{5}{3}a^{2}+5a-\frac{16}{3}\right){x}^{2}+\left(-\frac{31}{3}a^{3}+\frac{58}{3}a^{2}+73a-\frac{266}{3}\right){x}+\frac{182}{3}a^{3}-\frac{311}{3}a^{2}-426a+\frac{1462}{3}$ |
| 1.1-a5 |
1.1-a |
$6$ |
$8$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.21575$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$2576.572294$ |
1.177988192 |
\( 8000 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + \frac{2}{3}\) , \( \frac{2}{3} a^{3} - \frac{5}{3} a^{2} - 5 a + \frac{22}{3}\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + \frac{5}{3}\) , \( -\frac{28}{3} a^{3} + \frac{49}{3} a^{2} + 66 a - \frac{230}{3}\) , \( -\frac{212}{3} a^{3} + \frac{365}{3} a^{2} + 496 a - \frac{1720}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+\frac{2}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+\frac{5}{3}\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{5}{3}a^{2}-5a+\frac{22}{3}\right){x}^{2}+\left(-\frac{28}{3}a^{3}+\frac{49}{3}a^{2}+66a-\frac{230}{3}\right){x}-\frac{212}{3}a^{3}+\frac{365}{3}a^{2}+496a-\frac{1720}{3}$ |
| 1.1-a6 |
1.1-a |
$6$ |
$8$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$12.21575$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-32$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$644.1430735$ |
1.177988192 |
\( \frac{18473000}{3} a^{3} - \frac{18473000}{3} a^{2} - 36946000 a + \frac{115321000}{3} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 3 a - \frac{14}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 3 a - \frac{14}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 3 a - \frac{17}{3}\) , \( -\frac{2}{3} a^{3} + \frac{41}{3} a^{2} + 16 a - \frac{94}{3}\) , \( -2 a^{3} + 40 a^{2} + 35 a - 79\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+3a-\frac{14}{3}\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+3a-\frac{17}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+3a-\frac{14}{3}\right){x}^{2}+\left(-\frac{2}{3}a^{3}+\frac{41}{3}a^{2}+16a-\frac{94}{3}\right){x}-2a^{3}+40a^{2}+35a-79$ |
| 16.1-a1 |
16.1-a |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$17.27567$ |
$(2/3a^3-5/3a^2-3a+16/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.285450274$ |
$446.9898667$ |
3.733418898 |
\( \frac{2048}{3} a^{3} - \frac{2048}{3} a^{2} - 4096 a - \frac{5120}{3} \) |
\( \bigl[0\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - a + \frac{2}{3}\) , \( a^{2} - 4\) , \( a^{2} - 3\) , \( -a - 2\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-a+\frac{2}{3}\right){x}^{2}+\left(a^{2}-3\right){x}-a-2$ |
| 16.1-b1 |
16.1-b |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{30} \) |
$17.27567$ |
$(2/3a^3-5/3a^2-3a+16/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Nn |
$1$ |
\( 2 \) |
$1$ |
$132.3705092$ |
1.936599531 |
\( -\frac{7047}{32} a^{3} + \frac{7047}{32} a^{2} + \frac{21141}{16} a - \frac{6831}{8} \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} + a - 4\) , \( a\) , \( -\frac{11}{3} a^{3} - \frac{1}{3} a^{2} + 45 a + \frac{173}{3}\) , \( -69 a^{3} - 161 a^{2} + 244 a + 545\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+a{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-\frac{11}{3}a^{3}-\frac{1}{3}a^{2}+45a+\frac{173}{3}\right){x}-69a^{3}-161a^{2}+244a+545$ |
| 16.1-c1 |
16.1-c |
$2$ |
$3$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$17.27567$ |
$(2/3a^3-5/3a^2-3a+16/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$366.3450668$ |
2.679840430 |
\( \frac{14532608}{3} a^{3} - \frac{35815424}{3} a^{2} - 19021824 a + \frac{82542592}{3} \) |
\( \bigl[0\) , \( -\frac{2}{3} a^{3} + \frac{5}{3} a^{2} + 3 a - \frac{22}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{14}{3}\) , \( a^{2} + 2\) , \( -\frac{2}{3} a^{3} - \frac{1}{3} a^{2} + 2 a - \frac{7}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{14}{3}\right){y}={x}^{3}+\left(-\frac{2}{3}a^{3}+\frac{5}{3}a^{2}+3a-\frac{22}{3}\right){x}^{2}+\left(a^{2}+2\right){x}-\frac{2}{3}a^{3}-\frac{1}{3}a^{2}+2a-\frac{7}{3}$ |
| 16.1-c2 |
16.1-c |
$2$ |
$3$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$17.27567$ |
$(2/3a^3-5/3a^2-3a+16/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$366.3450668$ |
2.679840430 |
\( \frac{10387456}{3} a^{3} + \frac{10895360}{3} a^{2} - 30818304 a - \frac{138575872}{3} \) |
\( \bigl[0\) , \( \frac{2}{3} a^{3} - \frac{5}{3} a^{2} - 3 a + \frac{16}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{14}{3}\) , \( a^{2} - 4 a + 2\) , \( a^{3} - 3 a^{2} - 4 a + 6\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{14}{3}\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{5}{3}a^{2}-3a+\frac{16}{3}\right){x}^{2}+\left(a^{2}-4a+2\right){x}+a^{3}-3a^{2}-4a+6$ |
| 16.1-d1 |
16.1-d |
$2$ |
$3$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$17.27567$ |
$(2/3a^3-5/3a^2-3a+16/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$131.7458988$ |
0.963730695 |
\( \frac{10387456}{3} a^{3} + \frac{10895360}{3} a^{2} - 30818304 a - \frac{138575872}{3} \) |
\( \bigl[0\) , \( -\frac{2}{3} a^{3} + \frac{5}{3} a^{2} + 3 a - \frac{16}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{14}{3}\) , \( a^{2} - 4 a + 2\) , \( -a^{3} + 2 a^{2} + 4 a - 6\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{14}{3}\right){y}={x}^{3}+\left(-\frac{2}{3}a^{3}+\frac{5}{3}a^{2}+3a-\frac{16}{3}\right){x}^{2}+\left(a^{2}-4a+2\right){x}-a^{3}+2a^{2}+4a-6$ |
| 16.1-d2 |
16.1-d |
$2$ |
$3$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$17.27567$ |
$(2/3a^3-5/3a^2-3a+16/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$131.7458988$ |
0.963730695 |
\( \frac{14532608}{3} a^{3} - \frac{35815424}{3} a^{2} - 19021824 a + \frac{82542592}{3} \) |
\( \bigl[0\) , \( \frac{2}{3} a^{3} - \frac{5}{3} a^{2} - 3 a + \frac{22}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{14}{3}\) , \( a^{2} + 2\) , \( \frac{2}{3} a^{3} - \frac{2}{3} a^{2} - 2 a + \frac{7}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{14}{3}\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{5}{3}a^{2}-3a+\frac{22}{3}\right){x}^{2}+\left(a^{2}+2\right){x}+\frac{2}{3}a^{3}-\frac{2}{3}a^{2}-2a+\frac{7}{3}$ |
| 16.1-e1 |
16.1-e |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{30} \) |
$17.27567$ |
$(2/3a^3-5/3a^2-3a+16/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Nn |
$1$ |
\( 2 \) |
$1$ |
$132.3705092$ |
1.936599531 |
\( -\frac{7047}{32} a^{3} + \frac{7047}{32} a^{2} + \frac{21141}{16} a - \frac{6831}{8} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - a + \frac{2}{3}\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + 2 a - \frac{2}{3}\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - a + \frac{2}{3}\) , \( -\frac{25}{3} a^{3} - \frac{47}{3} a^{2} + 44 a + \frac{241}{3}\) , \( 48 a^{3} + 97 a^{2} - 234 a - 446\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-a+\frac{2}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-a+\frac{2}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+2a-\frac{2}{3}\right){x}^{2}+\left(-\frac{25}{3}a^{3}-\frac{47}{3}a^{2}+44a+\frac{241}{3}\right){x}+48a^{3}+97a^{2}-234a-446$ |
| 16.1-f1 |
16.1-f |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$17.27567$ |
$(2/3a^3-5/3a^2-3a+16/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.285450274$ |
$446.9898667$ |
3.733418898 |
\( \frac{2048}{3} a^{3} - \frac{2048}{3} a^{2} - 4096 a - \frac{5120}{3} \) |
\( \bigl[0\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + a - \frac{2}{3}\) , \( a^{2} - 4\) , \( a^{2} - 3\) , \( -a^{2} - a + 1\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+a-\frac{2}{3}\right){x}^{2}+\left(a^{2}-3\right){x}-a^{2}-a+1$ |
| 32.1-a1 |
32.1-a |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$18.83925$ |
$(2/3a^3-5/3a^2-3a+16/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$106.4402795$ |
1.557236553 |
\( 1536 a^{3} - 4096 a^{2} - 5120 a + 9728 \) |
\( \bigl[0\) , \( -a^{2} + 4\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{14}{3}\) , \( a^{3} - a^{2} - 2 a + 5\) , \( -4 a^{2} - 2 a + 7\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{14}{3}\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(a^{3}-a^{2}-2a+5\right){x}-4a^{2}-2a+7$ |
| 32.1-b1 |
32.1-b |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$18.83925$ |
$(2/3a^3-5/3a^2-3a+16/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.048265991$ |
$1283.889173$ |
3.626413700 |
\( -2048 a^{3} - 10240 a^{2} - 2048 a + 16384 \) |
\( \bigl[0\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{14}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{14}{3}\) , \( -\frac{11}{3} a^{3} + \frac{20}{3} a^{2} + 26 a - \frac{82}{3}\) , \( \frac{175}{3} a^{3} - \frac{301}{3} a^{2} - 410 a + \frac{1409}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{14}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{14}{3}\right){x}^{2}+\left(-\frac{11}{3}a^{3}+\frac{20}{3}a^{2}+26a-\frac{82}{3}\right){x}+\frac{175}{3}a^{3}-\frac{301}{3}a^{2}-410a+\frac{1409}{3}$ |
| 32.1-c1 |
32.1-c |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$18.83925$ |
$(2/3a^3-5/3a^2-3a+16/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$134.3296673$ |
1.965262296 |
\( -22427093329920 a^{3} + 38682448709632 a^{2} + 157551104018432 a - 182037162795008 \) |
\( \bigl[0\) , \( -a^{2} + 4\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{14}{3}\) , \( -11 a^{3} + 20 a^{2} + 78 a - 92\) , \( \frac{125}{3} a^{3} - \frac{215}{3} a^{2} - 294 a + \frac{991}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{14}{3}\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-11a^{3}+20a^{2}+78a-92\right){x}+\frac{125}{3}a^{3}-\frac{215}{3}a^{2}-294a+\frac{991}{3}$ |
| 32.1-d1 |
32.1-d |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$18.83925$ |
$(2/3a^3-5/3a^2-3a+16/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.031420930$ |
$1128.661831$ |
4.150701047 |
\( 1536 a^{3} - 4096 a^{2} - 5120 a + 9728 \) |
\( \bigl[0\) , \( a^{2} - 4\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{14}{3}\) , \( a^{3} - a^{2} - 2 a + 5\) , \( 3 a^{2} + 2 a - 7\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{14}{3}\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(a^{3}-a^{2}-2a+5\right){x}+3a^{2}+2a-7$ |
| 32.1-e1 |
32.1-e |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$18.83925$ |
$(2/3a^3-5/3a^2-3a+16/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$76.95740961$ |
1.125897938 |
\( -2048 a^{3} - 10240 a^{2} - 2048 a + 16384 \) |
\( \bigl[0\) , \( \frac{1}{3} a^{3} - \frac{4}{3} a^{2} - 2 a + \frac{14}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{14}{3}\) , \( -\frac{11}{3} a^{3} + \frac{20}{3} a^{2} + 26 a - \frac{82}{3}\) , \( -\frac{175}{3} a^{3} + \frac{298}{3} a^{2} + 410 a - \frac{1409}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{14}{3}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{4}{3}a^{2}-2a+\frac{14}{3}\right){x}^{2}+\left(-\frac{11}{3}a^{3}+\frac{20}{3}a^{2}+26a-\frac{82}{3}\right){x}-\frac{175}{3}a^{3}+\frac{298}{3}a^{2}+410a-\frac{1409}{3}$ |
| 32.1-f1 |
32.1-f |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$18.83925$ |
$(2/3a^3-5/3a^2-3a+16/3)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
|
\( 2 \) |
$1$ |
$60.71151934$ |
4.594578668 |
\( -22427093329920 a^{3} + 38682448709632 a^{2} + 157551104018432 a - 182037162795008 \) |
\( \bigl[0\) , \( a^{2} - 4\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{14}{3}\) , \( -11 a^{3} + 20 a^{2} + 78 a - 92\) , \( -\frac{125}{3} a^{3} + \frac{212}{3} a^{2} + 294 a - \frac{991}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{14}{3}\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-11a^{3}+20a^{2}+78a-92\right){x}-\frac{125}{3}a^{3}+\frac{212}{3}a^{2}+294a-\frac{991}{3}$ |
| 32.1-g1 |
32.1-g |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$18.83925$ |
$(2/3a^3-5/3a^2-3a+16/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.031420930$ |
$1128.661831$ |
4.150701047 |
\( \frac{3584}{3} a^{3} + \frac{4096}{3} a^{2} - 11264 a - \frac{49664}{3} \) |
\( \bigl[0\) , \( \frac{2}{3} a^{3} - \frac{5}{3} a^{2} - 4 a + \frac{22}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{14}{3}\) , \( \frac{7}{3} a^{3} - \frac{7}{3} a^{2} - 18 a + \frac{23}{3}\) , \( 3 a^{3} - 7 a^{2} - 20 a + 34\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{14}{3}\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{5}{3}a^{2}-4a+\frac{22}{3}\right){x}^{2}+\left(\frac{7}{3}a^{3}-\frac{7}{3}a^{2}-18a+\frac{23}{3}\right){x}+3a^{3}-7a^{2}-20a+34$ |
| 32.1-h1 |
32.1-h |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$18.83925$ |
$(2/3a^3-5/3a^2-3a+16/3)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
|
\( 2 \) |
$1$ |
$60.71151934$ |
4.594578668 |
\( -\frac{11782025191424}{3} a^{3} - \frac{36984040947712}{3} a^{2} + 575506343936 a + \frac{52547682603008}{3} \) |
\( \bigl[0\) , \( \frac{2}{3} a^{3} - \frac{5}{3} a^{2} - 4 a + \frac{22}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{14}{3}\) , \( -a^{3} - 8 a^{2} - 6 a + 18\) , \( -\frac{22}{3} a^{3} - \frac{68}{3} a^{2} + \frac{100}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{14}{3}\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{5}{3}a^{2}-4a+\frac{22}{3}\right){x}^{2}+\left(-a^{3}-8a^{2}-6a+18\right){x}-\frac{22}{3}a^{3}-\frac{68}{3}a^{2}+\frac{100}{3}$ |
| 32.1-i1 |
32.1-i |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$18.83925$ |
$(2/3a^3-5/3a^2-3a+16/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$106.4402795$ |
1.557236553 |
\( \frac{3584}{3} a^{3} + \frac{4096}{3} a^{2} - 11264 a - \frac{49664}{3} \) |
\( \bigl[0\) , \( -\frac{2}{3} a^{3} + \frac{5}{3} a^{2} + 4 a - \frac{22}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{14}{3}\) , \( \frac{7}{3} a^{3} - \frac{7}{3} a^{2} - 18 a + \frac{23}{3}\) , \( -3 a^{3} + 6 a^{2} + 20 a - 34\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{14}{3}\right){y}={x}^{3}+\left(-\frac{2}{3}a^{3}+\frac{5}{3}a^{2}+4a-\frac{22}{3}\right){x}^{2}+\left(\frac{7}{3}a^{3}-\frac{7}{3}a^{2}-18a+\frac{23}{3}\right){x}-3a^{3}+6a^{2}+20a-34$ |
| 32.1-j1 |
32.1-j |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$18.83925$ |
$(2/3a^3-5/3a^2-3a+16/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$134.3296673$ |
1.965262296 |
\( -\frac{11782025191424}{3} a^{3} - \frac{36984040947712}{3} a^{2} + 575506343936 a + \frac{52547682603008}{3} \) |
\( \bigl[0\) , \( -\frac{2}{3} a^{3} + \frac{5}{3} a^{2} + 4 a - \frac{22}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{14}{3}\) , \( -a^{3} - 8 a^{2} - 6 a + 18\) , \( \frac{22}{3} a^{3} + \frac{65}{3} a^{2} - \frac{100}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{14}{3}\right){y}={x}^{3}+\left(-\frac{2}{3}a^{3}+\frac{5}{3}a^{2}+4a-\frac{22}{3}\right){x}^{2}+\left(-a^{3}-8a^{2}-6a+18\right){x}+\frac{22}{3}a^{3}+\frac{65}{3}a^{2}-\frac{100}{3}$ |
| 32.1-k1 |
32.1-k |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$18.83925$ |
$(2/3a^3-5/3a^2-3a+16/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$76.95740961$ |
1.125897938 |
\( -\frac{45056}{3} a^{3} + \frac{81920}{3} a^{2} + 104448 a - \frac{397312}{3} \) |
\( \bigl[0\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{20}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{14}{3}\) , \( -\frac{1}{3} a^{3} - \frac{8}{3} a^{2} - 2 a + \frac{28}{3}\) , \( -\frac{32}{3} a^{3} - \frac{94}{3} a^{2} + 4 a + \frac{122}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{14}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{20}{3}\right){x}^{2}+\left(-\frac{1}{3}a^{3}-\frac{8}{3}a^{2}-2a+\frac{28}{3}\right){x}-\frac{32}{3}a^{3}-\frac{94}{3}a^{2}+4a+\frac{122}{3}$ |
| 32.1-l1 |
32.1-l |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$18.83925$ |
$(2/3a^3-5/3a^2-3a+16/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.048265991$ |
$1283.889173$ |
3.626413700 |
\( -\frac{45056}{3} a^{3} + \frac{81920}{3} a^{2} + 104448 a - \frac{397312}{3} \) |
\( \bigl[0\) , \( \frac{1}{3} a^{3} - \frac{4}{3} a^{2} - 2 a + \frac{20}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{14}{3}\) , \( -\frac{1}{3} a^{3} - \frac{8}{3} a^{2} - 2 a + \frac{28}{3}\) , \( \frac{32}{3} a^{3} + \frac{91}{3} a^{2} - 4 a - \frac{122}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{14}{3}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{4}{3}a^{2}-2a+\frac{20}{3}\right){x}^{2}+\left(-\frac{1}{3}a^{3}-\frac{8}{3}a^{2}-2a+\frac{28}{3}\right){x}+\frac{32}{3}a^{3}+\frac{91}{3}a^{2}-4a-\frac{122}{3}$ |
| 34.1-a1 |
34.1-a |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
34.1 |
\( 2 \cdot 17 \) |
\( - 2^{21} \cdot 17^{3} \) |
$18.98256$ |
$(2/3a^3-5/3a^2-3a+16/3), (a^3-2a^2-5a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$1.526647211$ |
$26.45048772$ |
3.544640593 |
\( \frac{44663037623}{943296} a^{3} + \frac{6323321339}{117912} a^{2} - \frac{32197890281}{78608} a - \frac{73753039867}{117912} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{17}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + a - \frac{14}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 3 a - \frac{17}{3}\) , \( \frac{2}{3} a^{3} + \frac{28}{3} a^{2} - 17 a - \frac{194}{3}\) , \( \frac{19}{3} a^{3} + \frac{53}{3} a^{2} - 71 a - \frac{466}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{17}{3}\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+3a-\frac{17}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+a-\frac{14}{3}\right){x}^{2}+\left(\frac{2}{3}a^{3}+\frac{28}{3}a^{2}-17a-\frac{194}{3}\right){x}+\frac{19}{3}a^{3}+\frac{53}{3}a^{2}-71a-\frac{466}{3}$ |
| 34.1-b1 |
34.1-b |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
34.1 |
\( 2 \cdot 17 \) |
\( - 2^{7} \cdot 17 \) |
$18.98256$ |
$(2/3a^3-5/3a^2-3a+16/3), (a^3-2a^2-5a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$268.2216180$ |
1.962060367 |
\( -\frac{19420}{51} a^{3} + \frac{109763}{102} a^{2} + \frac{74215}{68} a - \frac{98024}{51} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + \frac{5}{3}\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 3 a + \frac{5}{3}\) , \( a^{2} - 4\) , \( a^{3} - 2 a^{2} - 8 a + 9\) , \( \frac{2}{3} a^{3} - \frac{5}{3} a^{2} - 6 a + \frac{13}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+\frac{5}{3}\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-3a+\frac{5}{3}\right){x}^{2}+\left(a^{3}-2a^{2}-8a+9\right){x}+\frac{2}{3}a^{3}-\frac{5}{3}a^{2}-6a+\frac{13}{3}$ |
| 34.1-c1 |
34.1-c |
$2$ |
$3$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
34.1 |
\( 2 \cdot 17 \) |
\( - 2^{3} \cdot 17 \) |
$18.98256$ |
$(2/3a^3-5/3a^2-3a+16/3), (a^3-2a^2-5a+5)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
|
\( 3 \) |
$1$ |
$37.01438787$ |
7.321740557 |
\( \frac{15826032343616275}{102} a^{3} + \frac{8304978726196315}{51} a^{2} - \frac{46942536861493547}{34} a - \frac{105553740200159630}{51} \) |
\( \bigl[1\) , \( -\frac{2}{3} a^{3} + \frac{5}{3} a^{2} + 4 a - \frac{19}{3}\) , \( a^{2} - 5\) , \( -\frac{358}{3} a^{3} + \frac{619}{3} a^{2} + 838 a - \frac{2921}{3}\) , \( \frac{5377}{3} a^{3} - \frac{9274}{3} a^{2} - 12590 a + \frac{43613}{3}\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-\frac{2}{3}a^{3}+\frac{5}{3}a^{2}+4a-\frac{19}{3}\right){x}^{2}+\left(-\frac{358}{3}a^{3}+\frac{619}{3}a^{2}+838a-\frac{2921}{3}\right){x}+\frac{5377}{3}a^{3}-\frac{9274}{3}a^{2}-12590a+\frac{43613}{3}$ |
| 34.1-c2 |
34.1-c |
$2$ |
$3$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
34.1 |
\( 2 \cdot 17 \) |
\( - 2^{9} \cdot 17^{3} \) |
$18.98256$ |
$(2/3a^3-5/3a^2-3a+16/3), (a^3-2a^2-5a+5)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
|
\( 3^{2} \) |
$1$ |
$37.01438787$ |
7.321740557 |
\( -\frac{4833714366733173364724209}{117912} a^{3} + \frac{2084308311137971558039141}{29478} a^{2} + \frac{5659501685573404252148327}{19652} a - \frac{9808623393478752721965779}{29478} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + \frac{5}{3}\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 3 a + \frac{5}{3}\) , \( a^{2} + a - 5\) , \( -\frac{982}{3} a^{3} + \frac{1906}{3} a^{2} + 2112 a - \frac{8327}{3}\) , \( 5841 a^{3} - 10191 a^{2} - 39927 a + 45069\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+\frac{5}{3}\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-3a+\frac{5}{3}\right){x}^{2}+\left(-\frac{982}{3}a^{3}+\frac{1906}{3}a^{2}+2112a-\frac{8327}{3}\right){x}+5841a^{3}-10191a^{2}-39927a+45069$ |
| 34.1-d1 |
34.1-d |
$2$ |
$3$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
34.1 |
\( 2 \cdot 17 \) |
\( - 2^{9} \cdot 17^{3} \) |
$18.98256$ |
$(2/3a^3-5/3a^2-3a+16/3), (a^3-2a^2-5a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$36$ |
\( 1 \) |
$1$ |
$2.769334070$ |
0.729283582 |
\( -\frac{4833714366733173364724209}{117912} a^{3} + \frac{2084308311137971558039141}{29478} a^{2} + \frac{5659501685573404252148327}{19652} a - \frac{9808623393478752721965779}{29478} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{17}{3}\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - a - \frac{1}{3}\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - a + \frac{2}{3}\) , \( -329 a^{3} + 640 a^{2} + 2124 a - 2792\) , \( -\frac{19550}{3} a^{3} + \frac{33977}{3} a^{2} + 44750 a - \frac{151510}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{17}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-a+\frac{2}{3}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-a-\frac{1}{3}\right){x}^{2}+\left(-329a^{3}+640a^{2}+2124a-2792\right){x}-\frac{19550}{3}a^{3}+\frac{33977}{3}a^{2}+44750a-\frac{151510}{3}$ |
| 34.1-d2 |
34.1-d |
$2$ |
$3$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
34.1 |
\( 2 \cdot 17 \) |
\( - 2^{3} \cdot 17 \) |
$18.98256$ |
$(2/3a^3-5/3a^2-3a+16/3), (a^3-2a^2-5a+5)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$224.3160597$ |
0.729283582 |
\( \frac{15826032343616275}{102} a^{3} + \frac{8304978726196315}{51} a^{2} - \frac{46942536861493547}{34} a - \frac{105553740200159630}{51} \) |
\( \bigl[a^{2} - 5\) , \( \frac{2}{3} a^{3} - \frac{5}{3} a^{2} - 5 a + \frac{19}{3}\) , \( a^{2} - 4\) , \( -118 a^{3} + 203 a^{2} + 828 a - 964\) , \( -1911 a^{3} + 3296 a^{2} + 13422 a - 15510\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{5}{3}a^{2}-5a+\frac{19}{3}\right){x}^{2}+\left(-118a^{3}+203a^{2}+828a-964\right){x}-1911a^{3}+3296a^{2}+13422a-15510$ |
| 34.1-e1 |
34.1-e |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
34.1 |
\( 2 \cdot 17 \) |
\( - 2^{7} \cdot 17 \) |
$18.98256$ |
$(2/3a^3-5/3a^2-3a+16/3), (a^3-2a^2-5a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 7 \) |
$0.025279685$ |
$1133.316262$ |
5.868125557 |
\( -\frac{19420}{51} a^{3} + \frac{109763}{102} a^{2} + \frac{74215}{68} a - \frac{98024}{51} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{17}{3}\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - a - \frac{1}{3}\) , \( 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - a + \frac{2}{3}\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{1}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{17}{3}\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-a-\frac{1}{3}\right){x}^{2}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-a+\frac{2}{3}\right){x}+\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{1}{3}$ |
| 34.1-f1 |
34.1-f |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
34.1 |
\( 2 \cdot 17 \) |
\( - 2^{21} \cdot 17^{3} \) |
$18.98256$ |
$(2/3a^3-5/3a^2-3a+16/3), (a^3-2a^2-5a+5)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3^{2} \cdot 7 \) |
$0.002345028$ |
$447.0602657$ |
7.730246776 |
\( \frac{44663037623}{943296} a^{3} + \frac{6323321339}{117912} a^{2} - \frac{32197890281}{78608} a - \frac{73753039867}{117912} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + \frac{5}{3}\) , \( -a^{2} + a + 4\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 3 a - \frac{14}{3}\) , \( \frac{7}{3} a^{3} + \frac{14}{3} a^{2} - 26 a - \frac{136}{3}\) , \( -6 a^{3} - 10 a^{2} + 56 a + 94\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+\frac{5}{3}\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+3a-\frac{14}{3}\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(\frac{7}{3}a^{3}+\frac{14}{3}a^{2}-26a-\frac{136}{3}\right){x}-6a^{3}-10a^{2}+56a+94$ |
| 34.2-a1 |
34.2-a |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
34.2 |
\( 2 \cdot 17 \) |
\( - 2^{21} \cdot 17^{3} \) |
$18.98256$ |
$(2/3a^3-5/3a^2-3a+16/3), (-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$1.526647211$ |
$26.45048772$ |
3.544640593 |
\( \frac{68697290635}{943296} a^{3} - \frac{81973449485}{471648} a^{2} - \frac{3060284231}{9826} a + \frac{205270135219}{471648} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{17}{3}\) , \( -a^{2} + a + 6\) , \( a^{2} + a - 5\) , \( \frac{10}{3} a^{3} - \frac{40}{3} a^{2} - 9 a + \frac{122}{3}\) , \( 12 a^{3} - 37 a^{2} - 41 a + 100\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{17}{3}\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(\frac{10}{3}a^{3}-\frac{40}{3}a^{2}-9a+\frac{122}{3}\right){x}+12a^{3}-37a^{2}-41a+100$ |
| 34.2-b1 |
34.2-b |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
34.2 |
\( 2 \cdot 17 \) |
\( - 2^{7} \cdot 17 \) |
$18.98256$ |
$(2/3a^3-5/3a^2-3a+16/3), (-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$268.2216180$ |
1.962060367 |
\( -\frac{64261}{204} a^{3} - \frac{77585}{204} a^{2} + \frac{209667}{68} a + \frac{526601}{102} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + \frac{5}{3}\) , \( a + 1\) , \( a^{2} - 4\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + \frac{8}{3}\) , \( -2\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+\frac{5}{3}\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+\frac{8}{3}\right){x}-2$ |
| 34.2-c1 |
34.2-c |
$2$ |
$3$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
34.2 |
\( 2 \cdot 17 \) |
\( - 2^{3} \cdot 17 \) |
$18.98256$ |
$(2/3a^3-5/3a^2-3a+16/3), (-a-3)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
|
\( 3 \) |
$1$ |
$37.01438787$ |
7.321740557 |
\( \frac{11079776683347274}{51} a^{3} - \frac{54595543162703453}{102} a^{2} - \frac{29028634559128099}{34} a + \frac{62959729802963168}{51} \) |
\( \bigl[1\) , \( -a^{2} + 5\) , \( a^{2} - 5\) , \( -\frac{61}{3} a^{3} - \frac{203}{3} a^{2} + \frac{298}{3}\) , \( \frac{944}{3} a^{3} + \frac{2953}{3} a^{2} - 54 a - \frac{4223}{3}\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-\frac{61}{3}a^{3}-\frac{203}{3}a^{2}+\frac{298}{3}\right){x}+\frac{944}{3}a^{3}+\frac{2953}{3}a^{2}-54a-\frac{4223}{3}$ |
| 34.2-c2 |
34.2-c |
$2$ |
$3$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
34.2 |
\( 2 \cdot 17 \) |
\( - 2^{9} \cdot 17^{3} \) |
$18.98256$ |
$(2/3a^3-5/3a^2-3a+16/3), (-a-3)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
|
\( 3^{2} \) |
$1$ |
$37.01438787$ |
7.321740557 |
\( -\frac{846460477173569678254403}{117912} a^{3} - \frac{332132300080642898647244}{14739} a^{2} + \frac{20673158333338790830285}{19652} a + \frac{1887601491695662579700023}{58956} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + \frac{5}{3}\) , \( a + 1\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 3 a - \frac{17}{3}\) , \( -\frac{214}{3} a^{3} - \frac{716}{3} a^{2} + 277 a + \frac{2482}{3}\) , \( \frac{3944}{3} a^{3} + \frac{9103}{3} a^{2} - 3009 a - \frac{22433}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+\frac{5}{3}\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+3a-\frac{17}{3}\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-\frac{214}{3}a^{3}-\frac{716}{3}a^{2}+277a+\frac{2482}{3}\right){x}+\frac{3944}{3}a^{3}+\frac{9103}{3}a^{2}-3009a-\frac{22433}{3}$ |
| 34.2-d1 |
34.2-d |
$2$ |
$3$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
34.2 |
\( 2 \cdot 17 \) |
\( - 2^{9} \cdot 17^{3} \) |
$18.98256$ |
$(2/3a^3-5/3a^2-3a+16/3), (-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$36$ |
\( 1 \) |
$1$ |
$2.769334070$ |
0.729283582 |
\( -\frac{846460477173569678254403}{117912} a^{3} - \frac{332132300080642898647244}{14739} a^{2} + \frac{20673158333338790830285}{19652} a + \frac{1887601491695662579700023}{58956} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{17}{3}\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + a - \frac{5}{3}\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - a + \frac{2}{3}\) , \( -\frac{218}{3} a^{3} - \frac{709}{3} a^{2} + 283 a + \frac{2456}{3}\) , \( -\frac{4162}{3} a^{3} - \frac{9815}{3} a^{2} + 3294 a + \frac{24886}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{17}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-a+\frac{2}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+a-\frac{5}{3}\right){x}^{2}+\left(-\frac{218}{3}a^{3}-\frac{709}{3}a^{2}+283a+\frac{2456}{3}\right){x}-\frac{4162}{3}a^{3}-\frac{9815}{3}a^{2}+3294a+\frac{24886}{3}$ |
| 34.2-d2 |
34.2-d |
$2$ |
$3$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
34.2 |
\( 2 \cdot 17 \) |
\( - 2^{3} \cdot 17 \) |
$18.98256$ |
$(2/3a^3-5/3a^2-3a+16/3), (-a-3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$224.3160597$ |
0.729283582 |
\( \frac{11079776683347274}{51} a^{3} - \frac{54595543162703453}{102} a^{2} - \frac{29028634559128099}{34} a + \frac{62959729802963168}{51} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 5\) , \( a^{2} - 4\) , \( -\frac{61}{3} a^{3} - \frac{197}{3} a^{2} - 2 a + \frac{259}{3}\) , \( -335 a^{3} - 1051 a^{2} + 52 a + 1497\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-\frac{61}{3}a^{3}-\frac{197}{3}a^{2}-2a+\frac{259}{3}\right){x}-335a^{3}-1051a^{2}+52a+1497$ |
| 34.2-e1 |
34.2-e |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
34.2 |
\( 2 \cdot 17 \) |
\( - 2^{7} \cdot 17 \) |
$18.98256$ |
$(2/3a^3-5/3a^2-3a+16/3), (-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 7 \) |
$0.025279685$ |
$1133.316262$ |
5.868125557 |
\( -\frac{64261}{204} a^{3} - \frac{77585}{204} a^{2} + \frac{209667}{68} a + \frac{526601}{102} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{17}{3}\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + a - \frac{5}{3}\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + \frac{5}{3}\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 4 a + \frac{11}{3}\) , \( -a + 1\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{17}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+\frac{5}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+a-\frac{5}{3}\right){x}^{2}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-4a+\frac{11}{3}\right){x}-a+1$ |
| 34.2-f1 |
34.2-f |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
34.2 |
\( 2 \cdot 17 \) |
\( - 2^{21} \cdot 17^{3} \) |
$18.98256$ |
$(2/3a^3-5/3a^2-3a+16/3), (-a-3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3^{2} \cdot 7 \) |
$0.002345028$ |
$447.0602657$ |
7.730246776 |
\( \frac{68697290635}{943296} a^{3} - \frac{81973449485}{471648} a^{2} - \frac{3060284231}{9826} a + \frac{205270135219}{471648} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + \frac{5}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + a - \frac{20}{3}\) , \( a^{2} + a - 4\) , \( 4 a^{3} - 13 a^{2} - 15 a + 37\) , \( -9 a^{3} + 23 a^{2} + 31 a - 63\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+\frac{5}{3}\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+a-\frac{20}{3}\right){x}^{2}+\left(4a^{3}-13a^{2}-15a+37\right){x}-9a^{3}+23a^{2}+31a-63$ |
| 41.3-a1 |
41.3-a |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
41.3 |
\( 41 \) |
\( 41^{2} \) |
$19.43202$ |
$(1/3a^3+5/3a^2-13/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.523055922$ |
$71.90723577$ |
2.201046879 |
\( -\frac{331998410}{5043} a^{3} - \frac{1336007743}{5043} a^{2} - \frac{49646647}{1681} a + \frac{2014094435}{5043} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + \frac{5}{3}\) , \( \frac{2}{3} a^{3} - \frac{5}{3} a^{2} - 5 a + \frac{16}{3}\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - a + \frac{5}{3}\) , \( \frac{8}{3} a^{3} - \frac{17}{3} a^{2} - 15 a + \frac{58}{3}\) , \( 3 a^{3} - 7 a^{2} - 18 a + 23\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+\frac{5}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-a+\frac{5}{3}\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{5}{3}a^{2}-5a+\frac{16}{3}\right){x}^{2}+\left(\frac{8}{3}a^{3}-\frac{17}{3}a^{2}-15a+\frac{58}{3}\right){x}+3a^{3}-7a^{2}-18a+23$ |
| 41.3-b1 |
41.3-b |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
41.3 |
\( 41 \) |
\( 41^{2} \) |
$19.43202$ |
$(1/3a^3+5/3a^2-13/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.050898944$ |
$970.8568924$ |
2.891828724 |
\( -\frac{331998410}{5043} a^{3} - \frac{1336007743}{5043} a^{2} - \frac{49646647}{1681} a + \frac{2014094435}{5043} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{17}{3}\) , \( a^{2} + a - 4\) , \( a^{2} + a - 4\) , \( \frac{4}{3} a^{3} - \frac{1}{3} a^{2} - 2 a - \frac{4}{3}\) , \( -2 a^{3} + 8 a^{2} + 13 a - 21\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{17}{3}\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(\frac{4}{3}a^{3}-\frac{1}{3}a^{2}-2a-\frac{4}{3}\right){x}-2a^{3}+8a^{2}+13a-21$ |
| 41.4-a1 |
41.4-a |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
41.4 |
\( 41 \) |
\( 41^{2} \) |
$19.43202$ |
$(2/3a^3-2/3a^2-6a+13/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.523055922$ |
$71.90723577$ |
2.201046879 |
\( -\frac{2157645979}{5043} a^{3} + \frac{3825652132}{5043} a^{2} + \frac{5028935425}{1681} a - \frac{18317262233}{5043} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + \frac{5}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 3 a - \frac{20}{3}\) , \( a + 1\) , \( \frac{5}{3} a^{3} + \frac{1}{3} a^{2} - 12 a - \frac{20}{3}\) , \( a^{3} + 2 a^{2} - 7 a - 15\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+\frac{5}{3}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+3a-\frac{20}{3}\right){x}^{2}+\left(\frac{5}{3}a^{3}+\frac{1}{3}a^{2}-12a-\frac{20}{3}\right){x}+a^{3}+2a^{2}-7a-15$ |
| 41.4-b1 |
41.4-b |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
41.4 |
\( 41 \) |
\( 41^{2} \) |
$19.43202$ |
$(2/3a^3-2/3a^2-6a+13/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.050898944$ |
$970.8568924$ |
2.891828724 |
\( -\frac{2157645979}{5043} a^{3} + \frac{3825652132}{5043} a^{2} + \frac{5028935425}{1681} a - \frac{18317262233}{5043} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{17}{3}\) , \( -a^{2} - a + 6\) , \( a^{2} + a - 4\) , \( \frac{4}{3} a^{3} - \frac{4}{3} a^{2} - 13 a + \frac{5}{3}\) , \( \frac{1}{3} a^{3} - \frac{10}{3} a^{2} - 6 a + \frac{38}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{17}{3}\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(\frac{4}{3}a^{3}-\frac{4}{3}a^{2}-13a+\frac{5}{3}\right){x}+\frac{1}{3}a^{3}-\frac{10}{3}a^{2}-6a+\frac{38}{3}$ |
| 47.1-a1 |
47.1-a |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47^{2} \) |
$19.76661$ |
$(-2/3a^3+5/3a^2+3a-19/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$339.9519495$ |
4.973545770 |
\( \frac{43707803}{6627} a^{3} - \frac{143880386}{6627} a^{2} - \frac{7694349}{2209} a + \frac{142892701}{6627} \) |
\( \bigl[a + 1\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 3 a - \frac{14}{3}\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - a + \frac{5}{3}\) , \( 4 a^{3} - 6 a^{2} - 15 a + 18\) , \( 9 a^{3} - 17 a^{2} - 31 a + 41\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-a+\frac{5}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+3a-\frac{14}{3}\right){x}^{2}+\left(4a^{3}-6a^{2}-15a+18\right){x}+9a^{3}-17a^{2}-31a+41$ |
| 47.1-b1 |
47.1-b |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47^{2} \) |
$19.76661$ |
$(-2/3a^3+5/3a^2+3a-19/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.117012433$ |
$271.7661081$ |
1.860955045 |
\( \frac{43707803}{6627} a^{3} - \frac{143880386}{6627} a^{2} - \frac{7694349}{2209} a + \frac{142892701}{6627} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - a + \frac{5}{3}\) , \( -\frac{2}{3} a^{3} + \frac{5}{3} a^{2} + 5 a - \frac{16}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 3 a - \frac{14}{3}\) , \( 4 a^{3} - 5 a^{2} - 16 a + 19\) , \( -\frac{7}{3} a^{3} + \frac{40}{3} a^{2} + 18 a - \frac{92}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-a+\frac{5}{3}\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+3a-\frac{14}{3}\right){y}={x}^{3}+\left(-\frac{2}{3}a^{3}+\frac{5}{3}a^{2}+5a-\frac{16}{3}\right){x}^{2}+\left(4a^{3}-5a^{2}-16a+19\right){x}-\frac{7}{3}a^{3}+\frac{40}{3}a^{2}+18a-\frac{92}{3}$ |
| 47.2-a1 |
47.2-a |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
47.2 |
\( 47 \) |
\( 47^{2} \) |
$19.76661$ |
$(1/3a^3-1/3a^2-a+11/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$339.9519495$ |
4.973545770 |
\( \frac{18882446}{2209} a^{3} + \frac{14508415}{2209} a^{2} - \frac{193015933}{2209} a - \frac{277651353}{2209} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - a + \frac{5}{3}\) , \( a^{2} + a - 5\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 3 a - \frac{14}{3}\) , \( \frac{10}{3} a^{3} + \frac{14}{3} a^{2} - 20 a - \frac{76}{3}\) , \( \frac{14}{3} a^{3} + \frac{34}{3} a^{2} - 23 a - \frac{167}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-a+\frac{5}{3}\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+3a-\frac{14}{3}\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(\frac{10}{3}a^{3}+\frac{14}{3}a^{2}-20a-\frac{76}{3}\right){x}+\frac{14}{3}a^{3}+\frac{34}{3}a^{2}-23a-\frac{167}{3}$ |
| 47.2-b1 |
47.2-b |
$1$ |
$1$ |
4.4.18688.1 |
$4$ |
$[4, 0]$ |
47.2 |
\( 47 \) |
\( 47^{2} \) |
$19.76661$ |
$(1/3a^3-1/3a^2-a+11/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.117012433$ |
$271.7661081$ |
1.860955045 |
\( \frac{18882446}{2209} a^{3} + \frac{14508415}{2209} a^{2} - \frac{193015933}{2209} a - \frac{277651353}{2209} \) |
\( \bigl[a + 1\) , \( a^{2} + a - 6\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{14}{3}\) , \( \frac{8}{3} a^{3} + \frac{10}{3} a^{2} - 19 a - \frac{68}{3}\) , \( -6 a^{3} - 4 a^{2} + 61 a + 81\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+2a-\frac{14}{3}\right){y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(\frac{8}{3}a^{3}+\frac{10}{3}a^{2}-19a-\frac{68}{3}\right){x}-6a^{3}-4a^{2}+61a+81$ |
*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.
