| 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 |
| 10.2-a1 |
10.2-a |
$4$ |
$4$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{2} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.137508209$ |
$1860.615168$ |
5.455288409 |
\( \frac{281894497}{1600} a^{3} - \frac{641073513}{1600} a^{2} - \frac{232768723}{320} a + \frac{1784392217}{1600} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 6 a + 1\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 27 a^{3} - 81 a^{2} - 43 a + 139\) , \( -152 a^{3} + 424 a^{2} + 292 a - 653\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a+1\right){x}^{2}+\left(27a^{3}-81a^{2}-43a+139\right){x}-152a^{3}+424a^{2}+292a-653$ |
| 10.2-a2 |
10.2-a |
$4$ |
$4$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{4} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.275016418$ |
$465.1537920$ |
5.455288409 |
\( \frac{926146356449381}{5000} a^{3} - \frac{2117094157744749}{5000} a^{2} - \frac{752147055461879}{1000} a + \frac{5762277566448941}{5000} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 6 a + 1\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 62 a^{3} - 171 a^{2} - 123 a + 259\) , \( 292 a^{3} - 776 a^{2} - 623 a + 1099\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a+1\right){x}^{2}+\left(62a^{3}-171a^{2}-123a+259\right){x}+292a^{3}-776a^{2}-623a+1099$ |
| 10.2-a3 |
10.2-a |
$4$ |
$4$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{3} \cdot 5 \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.275016418$ |
$930.3075841$ |
5.455288409 |
\( \frac{15407}{40} a^{3} - \frac{28903}{40} a^{2} - \frac{11053}{8} a + \frac{88207}{40} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - 4\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( -5 a^{3} + 18 a^{2} + 25 a - 46\) , \( 10 a^{3} - 11 a^{2} - 32 a + 36\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-2a^{2}-3a+4\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-5a^{3}+18a^{2}+25a-46\right){x}+10a^{3}-11a^{2}-32a+36$ |
| 10.2-a4 |
10.2-a |
$4$ |
$4$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{12} \cdot 5 \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.068754104$ |
$930.3075841$ |
5.455288409 |
\( -\frac{5953141884539}{20480} a^{3} + \frac{16793324164371}{20480} a^{2} + \frac{2219102602241}{4096} a - \frac{26156605672419}{20480} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 5\) , \( a^{3} - 3 a^{2} - 4 a + 8\) , \( a^{3} - 2 a^{2} - 4 a + 4\) , \( -8 a^{3} - 31 a^{2} + 53\) , \( -90 a^{3} - 191 a^{2} + 103 a + 277\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+5\right){x}{y}+\left(a^{3}-2a^{2}-4a+4\right){y}={x}^{3}+\left(a^{3}-3a^{2}-4a+8\right){x}^{2}+\left(-8a^{3}-31a^{2}+53\right){x}-90a^{3}-191a^{2}+103a+277$ |
| 10.2-b1 |
10.2-b |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{2} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.064527244$ |
$1310.109571$ |
1.201688798 |
\( \frac{92624126421}{200} a^{3} + \frac{180375975491}{200} a^{2} - \frac{23344659439}{40} a - \frac{251401484819}{200} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a\) , \( -39 a^{3} + 104 a^{2} + 82 a - 147\) , \( 133 a^{3} - 381 a^{2} - 239 a + 605\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-39a^{3}+104a^{2}+82a-147\right){x}+133a^{3}-381a^{2}-239a+605$ |
| 10.2-b2 |
10.2-b |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{6} \cdot 5 \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.032263622$ |
$2620.219142$ |
1.201688798 |
\( \frac{5241983837}{320} a^{3} - \frac{12000242053}{320} a^{2} - \frac{4254963207}{64} a + \frac{32693132597}{320} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{3} - a^{2} - 5 a\) , \( 6 a^{3} - 12 a^{2} - 27 a + 26\) , \( 6 a^{3} - 15 a^{2} - 23 a + 44\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+5\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+5\right){x}^{2}+\left(6a^{3}-12a^{2}-27a+26\right){x}+6a^{3}-15a^{2}-23a+44$ |
| 10.2-c1 |
10.2-c |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5^{2} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$793.0373736$ |
2.818220285 |
\( \frac{156555109}{50} a^{3} - \frac{357773261}{50} a^{2} - \frac{127029151}{10} a + \frac{973277949}{50} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a^{2} - a - 3\) , \( -8 a^{2} + 16 a + 18\) , \( 13 a^{3} - 42 a^{2} - 22 a + 95\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(-8a^{2}+16a+18\right){x}+13a^{3}-42a^{2}-22a+95$ |
| 10.2-c2 |
10.2-c |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5 \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$793.0373736$ |
2.818220285 |
\( -\frac{2410883683}{20} a^{3} + \frac{6800672827}{20} a^{2} + \frac{898669113}{4} a - \frac{10592430283}{20} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{2} - a - 3\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 1\) , \( a^{3} + a^{2} - 3 a - 3\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+5\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+{x}+a^{3}+a^{2}-3a-3$ |
| 10.2-d1 |
10.2-d |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{14} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$0.261515903$ |
$59.10421161$ |
3.075996537 |
\( \frac{29263792417871110513}{390625000000} a^{3} - \frac{66892456727166401977}{390625000000} a^{2} - \frac{23766272438515846467}{78125000000} a + \frac{182062010179875460393}{390625000000} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + 3 a^{2} + 3 a - 7\) , \( a^{3} - a^{2} - 5 a\) , \( -8 a^{3} + 19 a^{2} + 32 a - 58\) , \( 56 a^{3} - 136 a^{2} - 197 a + 316\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+3a-7\right){x}^{2}+\left(-8a^{3}+19a^{2}+32a-58\right){x}+56a^{3}-136a^{2}-197a+316$ |
| 10.2-d2 |
10.2-d |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{3} \cdot 5^{7} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 7 \) |
$0.523031807$ |
$118.2084232$ |
3.075996537 |
\( -\frac{1267618337281}{625000} a^{3} + \frac{488374808849}{625000} a^{2} + \frac{2101610388979}{125000} a + \frac{9997063509159}{625000} \) |
\( \bigl[1\) , \( a^{3} - 2 a^{2} - 4 a + 3\) , \( a\) , \( -97 a^{3} - 193 a^{2} + 110 a + 257\) , \( -2269 a^{3} - 4424 a^{2} + 2845 a + 6149\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{3}-2a^{2}-4a+3\right){x}^{2}+\left(-97a^{3}-193a^{2}+110a+257\right){x}-2269a^{3}-4424a^{2}+2845a+6149$ |
| 10.2-e1 |
10.2-e |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{3} \cdot 5^{7} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$540.3329937$ |
0.960091828 |
\( -\frac{1267618337281}{625000} a^{3} + \frac{488374808849}{625000} a^{2} + \frac{2101610388979}{125000} a + \frac{9997063509159}{625000} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - 3 a^{2} - 3 a + 8\) , \( a^{3} - a^{2} - 5 a + 1\) , \( -33 a^{3} - 27 a^{2} + 66 a + 10\) , \( 222 a^{3} + 633 a^{2} - 148 a - 1028\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+8\right){x}^{2}+\left(-33a^{3}-27a^{2}+66a+10\right){x}+222a^{3}+633a^{2}-148a-1028$ |
| 10.2-e2 |
10.2-e |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{14} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$135.0832484$ |
0.960091828 |
\( \frac{29263792417871110513}{390625000000} a^{3} - \frac{66892456727166401977}{390625000000} a^{2} - \frac{23766272438515846467}{78125000000} a + \frac{182062010179875460393}{390625000000} \) |
\( \bigl[1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( 3 a^{3} - 23 a - 23\) , \( -16 a^{3} - 2 a^{2} + 107 a + 105\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-2a^{2}-3a+4\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(3a^{3}-23a-23\right){x}-16a^{3}-2a^{2}+107a+105$ |
| 10.2-f1 |
10.2-f |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5^{2} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.529285205$ |
$504.9325672$ |
3.798957290 |
\( \frac{156555109}{50} a^{3} - \frac{357773261}{50} a^{2} - \frac{127029151}{10} a + \frac{973277949}{50} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( a^{3} - 3 a^{2} - 4 a + 7\) , \( a^{3} - 2 a^{2} - 3 a + 5\) , \( 2 a^{3} - 8 a^{2} - 5 a + 28\) , \( 2 a^{3} - 7 a^{2} - 7 a + 25\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+\left(a^{3}-2a^{2}-3a+5\right){y}={x}^{3}+\left(a^{3}-3a^{2}-4a+7\right){x}^{2}+\left(2a^{3}-8a^{2}-5a+28\right){x}+2a^{3}-7a^{2}-7a+25$ |
| 10.2-f2 |
10.2-f |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5 \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.264642602$ |
$1009.865134$ |
3.798957290 |
\( -\frac{2410883683}{20} a^{3} + \frac{6800672827}{20} a^{2} + \frac{898669113}{4} a - \frac{10592430283}{20} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 4\) , \( a^{2} - 4\) , \( 0\) , \( -5 a^{3} - 12 a^{2} - 3 a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}-5a^{3}-12a^{2}-3a+4$ |
| 10.2-g1 |
10.2-g |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{2} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$142.4456807$ |
0.506209821 |
\( \frac{92624126421}{200} a^{3} + \frac{180375975491}{200} a^{2} - \frac{23344659439}{40} a - \frac{251401484819}{200} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( a^{3} - 3 a^{2} - 2 a + 9\) , \( a^{3} - 2 a^{2} - 4 a + 4\) , \( -46 a^{3} + 102 a^{2} + 191 a - 263\) , \( -378 a^{3} + 861 a^{2} + 1540 a - 2335\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+\left(a^{3}-2a^{2}-4a+4\right){y}={x}^{3}+\left(a^{3}-3a^{2}-2a+9\right){x}^{2}+\left(-46a^{3}+102a^{2}+191a-263\right){x}-378a^{3}+861a^{2}+1540a-2335$ |
| 10.2-g2 |
10.2-g |
$2$ |
$2$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{6} \cdot 5 \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$142.4456807$ |
0.506209821 |
\( \frac{5241983837}{320} a^{3} - \frac{12000242053}{320} a^{2} - \frac{4254963207}{64} a + \frac{32693132597}{320} \) |
\( \bigl[a + 1\) , \( a^{2} - 3\) , \( a^{3} - 2 a^{2} - 4 a + 4\) , \( -6 a^{3} + 16 a^{2} + 30 a - 45\) , \( -18 a^{3} + 45 a^{2} + 74 a - 119\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-2a^{2}-4a+4\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-6a^{3}+16a^{2}+30a-45\right){x}-18a^{3}+45a^{2}+74a-119$ |
| 10.2-h1 |
10.2-h |
$4$ |
$4$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{3} \cdot 5 \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$684.5604225$ |
3.649087925 |
\( \frac{15407}{40} a^{3} - \frac{28903}{40} a^{2} - \frac{11053}{8} a + \frac{88207}{40} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - a^{2} - 4 a\) , \( a^{3} - a^{2} - 5 a\) , \( a^{3} + a^{2} - 4 a - 4\) , \( a^{3} + 2 a^{2} - 4 a - 8\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(a^{3}+a^{2}-4a-4\right){x}+a^{3}+2a^{2}-4a-8$ |
| 10.2-h2 |
10.2-h |
$4$ |
$4$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{12} \cdot 5 \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$171.1401056$ |
3.649087925 |
\( -\frac{5953141884539}{20480} a^{3} + \frac{16793324164371}{20480} a^{2} + \frac{2219102602241}{4096} a - \frac{26156605672419}{20480} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{2} - a - 4\) , \( -23 a^{3} + 43 a^{2} + 87 a - 122\) , \( -176 a^{3} + 416 a^{2} + 724 a - 1124\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-4\right){x}^{2}+\left(-23a^{3}+43a^{2}+87a-122\right){x}-176a^{3}+416a^{2}+724a-1124$ |
| 10.2-h3 |
10.2-h |
$4$ |
$4$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{4} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$171.1401056$ |
3.649087925 |
\( \frac{926146356449381}{5000} a^{3} - \frac{2117094157744749}{5000} a^{2} - \frac{752147055461879}{1000} a + \frac{5762277566448941}{5000} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{2} - a - 3\) , \( -66 a^{3} + 178 a^{2} + 244 a - 545\) , \( -825 a^{3} + 1810 a^{2} + 3445 a - 4709\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+5\right){x}^{2}+\left(-66a^{3}+178a^{2}+244a-545\right){x}-825a^{3}+1810a^{2}+3445a-4709$ |
| 10.2-h4 |
10.2-h |
$4$ |
$4$ |
4.4.19796.1 |
$4$ |
$[4, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{2} \) |
$16.76592$ |
$(-a^2+2), (a^2+a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$684.5604225$ |
3.649087925 |
\( \frac{281894497}{1600} a^{3} - \frac{641073513}{1600} a^{2} - \frac{232768723}{320} a + \frac{1784392217}{1600} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{2} - a - 3\) , \( -a^{3} + 8 a^{2} + 4 a - 25\) , \( -17 a^{3} + 44 a^{2} + 73 a - 117\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+5\right){x}^{2}+\left(-a^{3}+8a^{2}+4a-25\right){x}-17a^{3}+44a^{2}+73a-117$ |
*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.
