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 |
196.2-a3 |
196.2-a |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{21} \cdot 7^{3} \) |
$0.88461$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.1.1[2] |
$1$ |
\( 2^{2} \cdot 7^{2} \) |
$1$ |
$2.509447298$ |
1.896963851 |
\( -\frac{1875341}{16384} a + \frac{29156511}{16384} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -5 a + 6\) , \( 2 a - 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a+6\right){x}+2a-1$ |
196.2-a4 |
196.2-a |
$4$ |
$14$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{21} \cdot 7^{3} \) |
$0.88461$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 7$ |
2B, 7B.1.1[2] |
$1$ |
\( 2^{2} \cdot 7^{2} \) |
$1$ |
$2.509447298$ |
1.896963851 |
\( \frac{1875341}{16384} a + \frac{13640585}{8192} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 4 a + 2\) , \( -3 a + 2\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(4a+2\right){x}-3a+2$ |
78.1-b2 |
78.1-b |
$4$ |
$14$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
78.1 |
\( 2 \cdot 3 \cdot 13 \) |
\( - 2^{7} \cdot 3^{14} \cdot 13^{2} \) |
$0.91993$ |
$(a+1), (a), (a-4)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7^{2} \) |
$1$ |
$5.816218741$ |
1.678997727 |
\( -\frac{2548644379963}{5913648} a + \frac{4423039769371}{5913648} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 32 a + 28\) , \( 28 a + 80\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(32a+28\right){x}+28a+80$ |
78.1-b3 |
78.1-b |
$4$ |
$14$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
78.1 |
\( 2 \cdot 3 \cdot 13 \) |
\( - 2^{14} \cdot 3^{7} \cdot 13 \) |
$0.91993$ |
$(a+1), (a), (a-4)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \cdot 7^{2} \) |
$1$ |
$11.63243748$ |
1.678997727 |
\( \frac{103368947}{134784} a + \frac{15792703}{22464} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -8 a - 12\) , \( 4 a + 8\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a-12\right){x}+4a+8$ |
78.2-b2 |
78.2-b |
$4$ |
$14$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
78.2 |
\( 2 \cdot 3 \cdot 13 \) |
\( - 2^{14} \cdot 3^{7} \cdot 13 \) |
$0.91993$ |
$(a+1), (a), (a+4)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \cdot 7^{2} \) |
$1$ |
$11.63243748$ |
1.678997727 |
\( -\frac{103368947}{134784} a + \frac{15792703}{22464} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 7 a - 12\) , \( -5 a + 8\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a-12\right){x}-5a+8$ |
78.2-b3 |
78.2-b |
$4$ |
$14$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
78.2 |
\( 2 \cdot 3 \cdot 13 \) |
\( - 2^{7} \cdot 3^{14} \cdot 13^{2} \) |
$0.91993$ |
$(a+1), (a), (a+4)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7^{2} \) |
$1$ |
$5.816218741$ |
1.678997727 |
\( \frac{2548644379963}{5913648} a + \frac{4423039769371}{5913648} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -33 a + 28\) , \( -29 a + 80\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-33a+28\right){x}-29a+80$ |
52.1-c2 |
52.1-c |
$4$ |
$14$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{21} \cdot 13^{2} \) |
$0.98938$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7^{2} \) |
$1$ |
$9.138615377$ |
2.216439792 |
\( -\frac{44029607}{2768896} a + \frac{22287093}{692224} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -12 a + 30\) , \( -153 a + 389\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-12a+30\right){x}-153a+389$ |
52.1-c3 |
52.1-c |
$4$ |
$14$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{21} \cdot 13 \) |
$0.98938$ |
$(-a+2), (-a-1), (-2a+3)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \cdot 7^{2} \) |
$1$ |
$18.27723075$ |
2.216439792 |
\( \frac{5011229819}{212992} a + \frac{11146070857}{212992} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -5 a - 13\) , \( 19 a + 33\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a-13\right){x}+19a+33$ |
52.2-c2 |
52.2-c |
$4$ |
$14$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
52.2 |
\( 2^{2} \cdot 13 \) |
\( 2^{21} \cdot 13^{2} \) |
$0.98938$ |
$(-a+2), (-a-1), (2a+1)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7^{2} \) |
$1$ |
$9.138615377$ |
2.216439792 |
\( \frac{44029607}{2768896} a + \frac{45118765}{2768896} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 11 a + 19\) , \( 152 a + 237\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(11a+19\right){x}+152a+237$ |
52.2-c3 |
52.2-c |
$4$ |
$14$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
52.2 |
\( 2^{2} \cdot 13 \) |
\( 2^{21} \cdot 13 \) |
$0.98938$ |
$(-a+2), (-a-1), (2a+1)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \cdot 7^{2} \) |
$1$ |
$18.27723075$ |
2.216439792 |
\( -\frac{5011229819}{212992} a + \frac{4039325169}{53248} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 6 a - 18\) , \( -15 a + 35\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-18\right){x}-15a+35$ |
348.1-d1 |
348.1-d |
$4$ |
$14$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
348.1 |
\( 2^{2} \cdot 3 \cdot 29 \) |
\( - 2^{28} \cdot 3^{7} \cdot 29 \) |
$2.21713$ |
$(-a-2), (-a+3), (-2a+7), (-2a+3)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7^{3} \) |
$1$ |
$4.947841567$ |
6.029160634 |
\( \frac{4525763593}{2405376} a - \frac{177195049787}{38486016} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -539 a - 1278\) , \( -254 a - 603\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-539a-1278\right){x}-254a-603$ |
348.1-d2 |
348.1-d |
$4$ |
$14$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
348.1 |
\( 2^{2} \cdot 3 \cdot 29 \) |
\( 2^{14} \cdot 3^{14} \cdot 29^{2} \) |
$2.21713$ |
$(-a-2), (-a+3), (-2a+7), (-2a+3)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7^{3} \) |
$1$ |
$4.947841567$ |
6.029160634 |
\( -\frac{490058940038863}{29428272} a + \frac{13272003184579649}{235426176} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -5659 a - 13438\) , \( 399234 a + 947109\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5659a-13438\right){x}+399234a+947109$ |
348.2-d1 |
348.2-d |
$4$ |
$14$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
348.2 |
\( 2^{2} \cdot 3 \cdot 29 \) |
\( - 2^{28} \cdot 3^{7} \cdot 29 \) |
$2.21713$ |
$(-a-2), (-a+3), (-2a+7), (2a+1)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7^{3} \) |
$1$ |
$4.947841567$ |
6.029160634 |
\( -\frac{4525763593}{2405376} a - \frac{104782832299}{38486016} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 540 a - 1817\) , \( 792 a - 2673\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(540a-1817\right){x}+792a-2673$ |
348.2-d4 |
348.2-d |
$4$ |
$14$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
348.2 |
\( 2^{2} \cdot 3 \cdot 29 \) |
\( 2^{14} \cdot 3^{14} \cdot 29^{2} \) |
$2.21713$ |
$(-a-2), (-a+3), (-2a+7), (2a+1)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7^{3} \) |
$1$ |
$4.947841567$ |
6.029160634 |
\( \frac{490058940038863}{29428272} a + \frac{3117177221422915}{78475392} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 5660 a - 19097\) , \( -393576 a + 1327247\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5660a-19097\right){x}-393576a+1327247$ |
49.1-a1 |
49.1-a |
$4$ |
$14$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{3} \) |
$1.19656$ |
$(-a^2-a+2)$ |
0 |
$\Z/14\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$7$ |
7B.1.1[3] |
$1$ |
\( 2 \) |
$1$ |
$354.0802648$ |
0.516151989 |
\( 16581375 \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - a - 3\) , \( a + 1\) , \( 62 a^{2} - 26 a - 156\) , \( -380 a^{2} + 192 a + 886\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(62a^{2}-26a-156\right){x}-380a^{2}+192a+886$ |
49.1-a2 |
49.1-a |
$4$ |
$14$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{3} \) |
$1.19656$ |
$(-a^2-a+2)$ |
0 |
$\Z/14\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$7$ |
7B.1.1[3] |
$1$ |
\( 2 \) |
$1$ |
$354.0802648$ |
0.516151989 |
\( -3375 \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - a - 3\) , \( a + 1\) , \( 2 a^{2} - a - 6\) , \( -9 a^{2} + 4 a + 20\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(2a^{2}-a-6\right){x}-9a^{2}+4a+20$ |
30.1-a3 |
30.1-a |
$4$ |
$14$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
30.1 |
\( 2 \cdot 3 \cdot 5 \) |
\( 2^{7} \cdot 3^{14} \cdot 5^{14} \) |
$4.42169$ |
$(a+1), (a), (a^2-2a-4)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7^{3} \) |
$1$ |
$12.37939177$ |
3.086983007 |
\( \frac{47202417142612573777}{233543408203125000} a^{2} + \frac{14757529767761610323}{23354340820312500} a + \frac{515886362451953206991}{233543408203125000} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 92 a^{2} - 138 a - 586\) , \( 296 a^{2} - 430 a - 1855\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(92a^{2}-138a-586\right){x}+296a^{2}-430a-1855$ |
30.1-a4 |
30.1-a |
$4$ |
$14$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
30.1 |
\( 2 \cdot 3 \cdot 5 \) |
\( - 2^{14} \cdot 3^{7} \cdot 5^{7} \) |
$4.42169$ |
$(a+1), (a), (a^2-2a-4)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \cdot 7^{3} \) |
$1$ |
$24.75878355$ |
3.086983007 |
\( -\frac{92595220954067}{5467500000} a^{2} + \frac{29028542654059}{1093500000} a + \frac{152066598768641}{1366875000} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 52 a^{2} - 78 a - 326\) , \( -316 a^{2} + 466 a + 1989\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(52a^{2}-78a-326\right){x}-316a^{2}+466a+1989$ |
8.1-c3 |
8.1-c |
$8$ |
$28$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{42} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7^{3} \) |
$1$ |
$22.62637536$ |
5.109181533 |
\( -\frac{162946107833949}{536870912} a^{2} + \frac{31406299407855}{536870912} a + \frac{417097255163391}{134217728} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 3104 a^{2} - 656 a - 31580\) , \( -208352 a^{2} + 44432 a + 2118431\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(3104a^{2}-656a-31580\right){x}-208352a^{2}+44432a+2118431$ |
8.1-c4 |
8.1-c |
$8$ |
$28$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{42} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7^{3} \) |
$1$ |
$22.62637536$ |
5.109181533 |
\( \frac{65769904213047}{536870912} a^{2} - \frac{260122311454851}{536870912} a + \frac{82276569972747}{268435456} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -200 a^{2} - 283 a + 1029\) , \( -2695 a^{2} - 4935 a + 10411\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-200a^{2}-283a+1029\right){x}-2695a^{2}-4935a+10411$ |
8.1-c6 |
8.1-c |
$8$ |
$28$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{42} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7^{3} \) |
$1$ |
$22.62637536$ |
5.109181533 |
\( \frac{48588101810451}{268435456} a^{2} + \frac{57179003011749}{134217728} a - \frac{13639816483965}{33554432} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -\frac{21177514163}{2} a^{2} - \frac{48646243987}{2} a + 25692521743\) , \( 1678001156646822 a^{2} + 3854487030340920 a - 4071495915100901\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-\frac{21177514163}{2}a^{2}-\frac{48646243987}{2}a+25692521743\right){x}+1678001156646822a^{2}+3854487030340920a-4071495915100901$ |
41.1-a3 |
41.1-a |
$4$ |
$14$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{2} \) |
$3.82741$ |
$(2a^2-a-3)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1706.734988$ |
0.646801491 |
\( \frac{4102114369346}{1681} a^{3} - \frac{5988741927479}{1681} a^{2} - \frac{9370177909896}{1681} a + \frac{8524056894480}{1681} \) |
\( \bigl[a + 1\) , \( -a^{3} + 2 a^{2} - 3\) , \( a + 1\) , \( -6 a^{3} + 16 a^{2} - 41\) , \( 21 a^{3} - 54 a^{2} - 19 a + 127\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}-3\right){x}^{2}+\left(-6a^{3}+16a^{2}-41\right){x}+21a^{3}-54a^{2}-19a+127$ |
41.1-a4 |
41.1-a |
$4$ |
$14$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$3.82741$ |
$(2a^2-a-3)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$3413.469977$ |
0.646801491 |
\( -\frac{1332303}{41} a^{3} + \frac{2252331}{41} a^{2} + \frac{2700811}{41} a - \frac{2683021}{41} \) |
\( \bigl[a + 1\) , \( -a^{3} + 2 a^{2} - 3\) , \( a + 1\) , \( -a^{3} + a^{2} - 1\) , \( -a^{2} + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}-3\right){x}^{2}+\left(-a^{3}+a^{2}-1\right){x}-a^{2}+3$ |
41.2-a2 |
41.2-a |
$4$ |
$14$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
41.2 |
\( 41 \) |
\( - 41^{2} \) |
$3.82741$ |
$(a^3-3a^2-a+4)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1706.734988$ |
0.646801491 |
\( \frac{1049537640009}{1681} a^{3} + \frac{837089918124}{1681} a^{2} - \frac{933126108814}{1681} a - \frac{188402509256}{1681} \) |
\( \bigl[a^{3} - a^{2} - a + 2\) , \( a^{3} - 4 a\) , \( 1\) , \( -5 a^{3} - 3 a^{2} + 20 a - 10\) , \( 2 a^{3} + 7 a^{2} - 18 a + 8\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-a+2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-5a^{3}-3a^{2}+20a-10\right){x}+2a^{3}+7a^{2}-18a+8$ |
41.2-a3 |
41.2-a |
$4$ |
$14$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
41.2 |
\( 41 \) |
\( 41 \) |
$3.82741$ |
$(a^3-3a^2-a+4)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$3413.469977$ |
0.646801491 |
\( -\frac{376070}{41} a^{3} - \frac{543958}{41} a^{2} + \frac{715935}{41} a + \frac{1033296}{41} \) |
\( \bigl[a^{3} - a^{2} - a + 2\) , \( a^{3} - 4 a\) , \( 1\) , \( 2 a^{2}\) , \( 2 a^{2} - a - 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-a+2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+2a^{2}{x}+2a^{2}-a-1$ |
145.1-d3 |
145.1-d |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{7} \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 7 \) |
$1$ |
$1003.116230$ |
1.068112419 |
\( \frac{20885181}{725} a^{3} - \frac{26043186}{725} a^{2} - \frac{78162292}{725} a + \frac{20490856}{145} \) |
\( \bigl[a + 1\) , \( a^{2} + a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a + 1\) , \( a^{3} + 2 a^{2} - 4 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(a^{3}-a+1\right){x}+a^{3}+2a^{2}-4a-1$ |
145.1-d4 |
145.1-d |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.1 |
\( 5 \cdot 29 \) |
\( 5^{14} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (-a^3-a^2+2a+3)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$250.7790575$ |
1.068112419 |
\( -\frac{57083181404}{525625} a^{3} + \frac{173419982887}{525625} a^{2} - \frac{106479911684}{525625} a - \frac{6075097893}{105125} \) |
\( \bigl[a + 1\) , \( a^{2} + a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - 15 a^{2} + 19 a + 6\) , \( -19 a^{3} + 48 a^{2} - 22 a - 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(a^{3}-15a^{2}+19a+6\right){x}-19a^{3}+48a^{2}-22a-7$ |
145.2-d3 |
145.2-d |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{14} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$250.7790575$ |
1.068112419 |
\( \frac{230503164291}{525625} a^{3} - \frac{277729455896}{525625} a^{2} - \frac{172985895152}{105125} a + \frac{1102426552392}{525625} \) |
\( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a + 1\) , \( -17 a^{3} + 22 a^{2} + 64 a - 84\) , \( 67 a^{3} - 79 a^{2} - 250 a + 314\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(-17a^{3}+22a^{2}+64a-84\right){x}+67a^{3}-79a^{2}-250a+314$ |
145.2-d4 |
145.2-d |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{7} \cdot 29 \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 7 \) |
$1$ |
$1003.116230$ |
1.068112419 |
\( -\frac{46928367}{725} a^{3} - \frac{15506749}{725} a^{2} + \frac{166828287}{725} a + \frac{34453039}{725} \) |
\( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a + 1\) , \( -2 a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{3} - a^{2} - 6 a + 6\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(-2a^{3}+2a^{2}+4a-4\right){x}+a^{3}-a^{2}-6a+6$ |
145.3-d3 |
145.3-d |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{14} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$250.7790575$ |
1.068112419 |
\( -\frac{508232620187}{525625} a^{3} - \frac{173419982887}{525625} a^{2} + \frac{1802427316457}{525625} a + \frac{385574986187}{525625} \) |
\( \bigl[a^{3} - 2 a\) , \( a^{2} - a - 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 36 a^{3} + 18 a^{2} - 134 a - 36\) , \( -153 a^{3} - 50 a^{2} + 535 a + 122\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(36a^{3}+18a^{2}-134a-36\right){x}-153a^{3}-50a^{2}+535a+122$ |
145.3-d4 |
145.3-d |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.3 |
\( 5 \cdot 29 \) |
\( 5^{7} \cdot 29 \) |
$5.58323$ |
$(-a-1), (-a^3+a^2+4a-2)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 7 \) |
$1$ |
$1003.116230$ |
1.068112419 |
\( \frac{31421618}{725} a^{3} + \frac{26043186}{725} a^{2} - \frac{15751621}{145} a - \frac{17225213}{725} \) |
\( \bigl[a^{3} - 2 a\) , \( a^{2} - a - 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + 3 a^{2} - 9 a - 1\) , \( -4 a^{3} + a^{2} + 10 a + 2\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(a^{3}+3a^{2}-9a-1\right){x}-4a^{3}+a^{2}+10a+2$ |
145.4-d1 |
145.4-d |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.4 |
\( 5 \cdot 29 \) |
\( 5^{7} \cdot 29 \) |
$5.58323$ |
$(-a-1), (2a^3+a^2-7a)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 7 \) |
$1$ |
$1003.116230$ |
1.068112419 |
\( -\frac{5378432}{725} a^{3} + \frac{15506749}{725} a^{2} - \frac{1981578}{145} a - \frac{1530771}{725} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 2 a - 2\) , \( a^{2} - 2\) , \( a^{3} + a^{2} - 2 a - 1\) , \( a^{3} + a^{2} - 2 a - 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-2a-2\right){x}^{2}+\left(a^{3}+a^{2}-2a-1\right){x}+a^{3}+a^{2}-2a-1$ |
145.4-d2 |
145.4-d |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.4 |
\( 5 \cdot 29 \) |
\( 5^{14} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (2a^3+a^2-7a)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$250.7790575$ |
1.068112419 |
\( \frac{13392505492}{21025} a^{3} + \frac{277729455896}{525625} a^{2} - \frac{831017929013}{525625} a - \frac{181911254079}{525625} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 2 a - 2\) , \( a^{2} - 2\) , \( -19 a^{3} - 19 a^{2} + 43 a + 14\) , \( 44 a^{3} + 39 a^{2} - 105 a - 26\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-2a-2\right){x}^{2}+\left(-19a^{3}-19a^{2}+43a+14\right){x}+44a^{3}+39a^{2}-105a-26$ |
1.1-a3 |
1.1-a |
$8$ |
$42$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$3.57436$ |
$\textsf{none}$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3, 7$ |
2B, 3B, 7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2222.133950$ |
0.283435452 |
\( 820352 a^{3} - 717600 a^{2} - 4294784 a + 3756992 \) |
\( \bigl[\frac{1}{2} a^{3} - a\) , \( \frac{1}{2} a^{3} - 2 a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a\) , \( \frac{1}{2} a^{2} + a - 1\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-2a\right){x}^{2}+\left(\frac{1}{2}a^{2}+a-1\right){x}$ |
1.1-a4 |
1.1-a |
$8$ |
$42$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$3.57436$ |
$\textsf{none}$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3, 7$ |
2B, 3B, 7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2222.133950$ |
0.283435452 |
\( -820352 a^{3} - 717600 a^{2} + 4294784 a + 3756992 \) |
\( \bigl[\frac{1}{2} a^{3} - a\) , \( -\frac{1}{2} a^{3} + 2 a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a\) , \( -a^{3} + \frac{1}{2} a^{2} - 1\) , \( -a^{3} + a\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a\right){x}^{2}+\left(-a^{3}+\frac{1}{2}a^{2}-1\right){x}-a^{3}+a$ |
1.1-a5 |
1.1-a |
$8$ |
$42$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$3.57436$ |
$\textsf{none}$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3, 7$ |
2B, 3B, 7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2222.133950$ |
0.283435452 |
\( 313664 a^{3} + 717600 a^{2} - 241280 a - 548608 \) |
\( \bigl[a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( \frac{1}{2} a^{2} + a - 1\) , \( \frac{1}{2} a^{3} - a^{2} + 1\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} + 1\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{2}+a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){x}^{2}+\left(\frac{1}{2}a^{3}-a^{2}+1\right){x}+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}+1$ |
1.1-a6 |
1.1-a |
$8$ |
$42$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$3.57436$ |
$\textsf{none}$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3, 7$ |
2B, 3B, 7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2222.133950$ |
0.283435452 |
\( -313664 a^{3} + 717600 a^{2} + 241280 a - 548608 \) |
\( \bigl[a\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a - 1\) , \( \frac{1}{2} a^{2} + a - 1\) , \( -a^{3} - a^{2} + a + 1\) , \( -a^{3} - \frac{3}{2} a^{2} + a + 1\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{2}+a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a-1\right){x}^{2}+\left(-a^{3}-a^{2}+a+1\right){x}-a^{3}-\frac{3}{2}a^{2}+a+1$ |
194.1-f2 |
194.1-f |
$4$ |
$14$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
194.1 |
\( 2 \cdot 97 \) |
\( 2^{14} \cdot 97 \) |
$8.28619$ |
$(a^3-4a+1), (-a^3-a^2+3a+6)$ |
$1$ |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$0.396225112$ |
$1474.622864$ |
3.477872677 |
\( \frac{9707873}{194} a^{3} + \frac{53426035}{1552} a^{2} - \frac{153162507}{776} a - \frac{162576597}{1552} \) |
\( \bigl[1\) , \( -a^{2} + a + 3\) , \( a\) , \( -3 a^{2} + 3 a + 3\) , \( -3 a^{3} + 5 a^{2} + a\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-3a^{2}+3a+3\right){x}-3a^{3}+5a^{2}+a$ |
194.1-f4 |
194.1-f |
$4$ |
$14$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
194.1 |
\( 2 \cdot 97 \) |
\( - 2^{7} \cdot 97^{2} \) |
$8.28619$ |
$(a^3-4a+1), (-a^3-a^2+3a+6)$ |
$1$ |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$0.792450224$ |
$737.3114322$ |
3.477872677 |
\( -\frac{390162372372957}{37636} a^{3} - \frac{188944457018475}{37636} a^{2} + \frac{718842047094221}{18818} a + \frac{370369171598017}{18818} \) |
\( \bigl[1\) , \( -a^{2} + a + 3\) , \( a\) , \( 10 a^{3} - 33 a^{2} + 33 a - 7\) , \( -127 a^{3} + 269 a^{2} - 19 a - 44\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(10a^{3}-33a^{2}+33a-7\right){x}-127a^{3}+269a^{2}-19a-44$ |
194.2-f1 |
194.2-f |
$4$ |
$14$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
194.2 |
\( 2 \cdot 97 \) |
\( - 2^{7} \cdot 97^{2} \) |
$8.28619$ |
$(a^3-4a+1), (2a^2-a-4)$ |
$1$ |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$0.792450224$ |
$737.3114322$ |
3.477872677 |
\( \frac{61482697651693}{18818} a^{3} + \frac{188944457018475}{37636} a^{2} - \frac{101699208840587}{37636} a - \frac{7519742438933}{18818} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{3} - 4 a\) , \( -74 a^{3} + 33 a^{2} + 286 a - 139\) , \( 527 a^{3} - 269 a^{2} - 1981 a + 1032\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-74a^{3}+33a^{2}+286a-139\right){x}+527a^{3}-269a^{2}-1981a+1032$ |
194.2-f3 |
194.2-f |
$4$ |
$14$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
194.2 |
\( 2 \cdot 97 \) |
\( 2^{14} \cdot 97 \) |
$8.28619$ |
$(a^3-4a+1), (2a^2-a-4)$ |
$1$ |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$0.396225112$ |
$1474.622864$ |
3.477872677 |
\( -\frac{2163461}{776} a^{3} - \frac{53426035}{1552} a^{2} - \frac{3772206}{97} a + \frac{51127543}{1552} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{3} - 4 a\) , \( -4 a^{3} + 3 a^{2} + 16 a - 9\) , \( 11 a^{3} - 5 a^{2} - 41 a + 20\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-4a^{3}+3a^{2}+16a-9\right){x}+11a^{3}-5a^{2}-41a+20$ |
194.3-f1 |
194.3-f |
$4$ |
$14$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
194.3 |
\( 2 \cdot 97 \) |
\( - 2^{7} \cdot 97^{2} \) |
$8.28619$ |
$(a^3-4a+1), (2a^2+a-4)$ |
$1$ |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$0.792450224$ |
$737.3114322$ |
3.477872677 |
\( -\frac{61482697651693}{18818} a^{3} + \frac{188944457018475}{37636} a^{2} + \frac{101699208840587}{37636} a - \frac{7519742438933}{18818} \) |
\( \bigl[1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{3} - 4 a\) , \( 73 a^{3} + 33 a^{2} - 282 a - 139\) , \( -527 a^{3} - 269 a^{2} + 1981 a + 1032\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(73a^{3}+33a^{2}-282a-139\right){x}-527a^{3}-269a^{2}+1981a+1032$ |
194.3-f3 |
194.3-f |
$4$ |
$14$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
194.3 |
\( 2 \cdot 97 \) |
\( 2^{14} \cdot 97 \) |
$8.28619$ |
$(a^3-4a+1), (2a^2+a-4)$ |
$1$ |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$0.396225112$ |
$1474.622864$ |
3.477872677 |
\( \frac{2163461}{776} a^{3} - \frac{53426035}{1552} a^{2} + \frac{3772206}{97} a + \frac{51127543}{1552} \) |
\( \bigl[1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{3} - 4 a\) , \( 3 a^{3} + 3 a^{2} - 12 a - 9\) , \( -11 a^{3} - 5 a^{2} + 41 a + 20\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(3a^{3}+3a^{2}-12a-9\right){x}-11a^{3}-5a^{2}+41a+20$ |
194.4-f2 |
194.4-f |
$4$ |
$14$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
194.4 |
\( 2 \cdot 97 \) |
\( 2^{14} \cdot 97 \) |
$8.28619$ |
$(a^3-4a+1), (-a^3+a^2+6a-1)$ |
$1$ |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$0.396225112$ |
$1474.622864$ |
3.477872677 |
\( -\frac{9707873}{194} a^{3} + \frac{53426035}{1552} a^{2} + \frac{153162507}{776} a - \frac{162576597}{1552} \) |
\( \bigl[1\) , \( -a^{2} - a + 3\) , \( a\) , \( -3 a^{2} - 4 a + 3\) , \( 3 a^{3} + 5 a^{2} - a\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-3a^{2}-4a+3\right){x}+3a^{3}+5a^{2}-a$ |
194.4-f4 |
194.4-f |
$4$ |
$14$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
194.4 |
\( 2 \cdot 97 \) |
\( - 2^{7} \cdot 97^{2} \) |
$8.28619$ |
$(a^3-4a+1), (-a^3+a^2+6a-1)$ |
$1$ |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$0.792450224$ |
$737.3114322$ |
3.477872677 |
\( \frac{390162372372957}{37636} a^{3} - \frac{188944457018475}{37636} a^{2} - \frac{718842047094221}{18818} a + \frac{370369171598017}{18818} \) |
\( \bigl[1\) , \( -a^{2} - a + 3\) , \( a\) , \( -10 a^{3} - 33 a^{2} - 34 a - 7\) , \( 127 a^{3} + 269 a^{2} + 19 a - 44\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-10a^{3}-33a^{2}-34a-7\right){x}+127a^{3}+269a^{2}+19a-44$ |
16.1-b2 |
16.1-b |
$4$ |
$14$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{17} \) |
$6.65950$ |
$(-a), (a^3-a^2-4a+1)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$1106.221345$ |
1.499429526 |
\( -\frac{1466589303347}{16384} a^{3} + \frac{255514832849}{16384} a^{2} + \frac{3038659044705}{8192} a + \frac{3551992972921}{16384} \) |
\( \bigl[a^{2} - 1\) , \( -a^{3} + 3 a\) , \( a\) , \( -4 a^{3} + 7 a^{2} + 11 a - 12\) , \( 3 a^{3} - 3 a^{2} - 7 a + 6\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+3a\right){x}^{2}+\left(-4a^{3}+7a^{2}+11a-12\right){x}+3a^{3}-3a^{2}-7a+6$ |
16.1-b3 |
16.1-b |
$4$ |
$14$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{13} \) |
$6.65950$ |
$(-a), (a^3-a^2-4a+1)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$1106.221345$ |
1.499429526 |
\( \frac{620979}{128} a^{3} - \frac{68657}{128} a^{2} - \frac{1152721}{64} a - \frac{1119033}{128} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 3 a^{3} - 3 a^{2} - 10 a + 3\) , \( -a^{3} + a^{2} + 3 a - 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-1\right){x}^{2}+\left(3a^{3}-3a^{2}-10a+3\right){x}-a^{3}+a^{2}+3a-1$ |
82.2-e2 |
82.2-e |
$4$ |
$14$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
82.2 |
\( 2 \cdot 41 \) |
\( - 2^{7} \cdot 41 \) |
$8.16871$ |
$(-a), (a^2+2a-1)$ |
$1$ |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 7 \) |
$0.487342794$ |
$2203.175622$ |
2.910701617 |
\( \frac{3579481083}{5248} a^{3} - \frac{5757410409}{5248} a^{2} - \frac{5527084921}{2624} a + \frac{11053893039}{5248} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + 4 a\) , \( a^{3} - 4 a\) , \( -2 a^{3} + 9 a + 1\) , \( -a^{3} + 2 a + 5\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(-2a^{3}+9a+1\right){x}-a^{3}+2a+5$ |
82.2-e4 |
82.2-e |
$4$ |
$14$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
82.2 |
\( 2 \cdot 41 \) |
\( 2^{14} \cdot 41^{2} \) |
$8.16871$ |
$(-a), (a^2+2a-1)$ |
$1$ |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7 \) |
$0.243671397$ |
$1101.587811$ |
2.910701617 |
\( -\frac{20809174087811}{27541504} a^{3} + \frac{4075020389185}{27541504} a^{2} + \frac{43592769056721}{13770752} a + \frac{50811214318441}{27541504} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 2 a^{2} - a + 3\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + 7 a^{2} - 2 a - 19\) , \( 3 a^{3} - 9 a^{2} - 5 a + 23\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-a+3\right){x}^{2}+\left(-a^{3}+7a^{2}-2a-19\right){x}+3a^{3}-9a^{2}-5a+23$ |
39.1-e2 |
39.1-e |
$4$ |
$14$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3^{7} \cdot 13^{2} \) |
$9.73778$ |
$(a^3-a^2-4a+1), (-a^3+a^2+2a-1)$ |
$1$ |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$0.371323934$ |
$1502.413729$ |
2.312257658 |
\( -\frac{5051534848}{1521} a^{3} + \frac{17683689664}{1521} a^{2} - \frac{869445632}{117} a - \frac{3355268992}{1521} \) |
\( \bigl[a^{2} - a - 1\) , \( a^{3} - a^{2} - 2 a\) , \( a^{2} - 1\) , \( -2 a^{3} - 3 a^{2} + 7 a + 1\) , \( 3 a^{2} - 3 a - 1\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a\right){x}^{2}+\left(-2a^{3}-3a^{2}+7a+1\right){x}+3a^{2}-3a-1$ |
*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.