| 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 |
| 16.3-a1 |
16.3-a |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$153.0558732$ |
1.507811580 |
\( -\frac{2142331909}{2} a^{3} + \frac{8913266161}{2} a^{2} - 2130537580 a - 3966334907 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{7}{2} a - 4\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( \frac{51}{2} a^{3} - 68 a^{2} - \frac{261}{2} a + 294\) , \( -\frac{68581}{2} a^{3} + \frac{184643}{2} a^{2} + 176121 a - 396257\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{7}{2}a-4\right){x}^{2}+\left(\frac{51}{2}a^{3}-68a^{2}-\frac{261}{2}a+294\right){x}-\frac{68581}{2}a^{3}+\frac{184643}{2}a^{2}+176121a-396257$ |
| 16.3-a2 |
16.3-a |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$153.0558732$ |
1.507811580 |
\( -\frac{728135853331382213}{2} a^{3} + \frac{224049360810344247}{2} a^{2} + 2738054551954718675 a + 1721058939374601181 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( 0\) , \( 9 a^{3} - 2 a^{2} - 66 a - 42\) , \( -\frac{99}{2} a^{3} + \frac{23}{2} a^{2} + 366 a + 230\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}^{2}+\left(9a^{3}-2a^{2}-66a-42\right){x}-\frac{99}{2}a^{3}+\frac{23}{2}a^{2}+366a+230$ |
| 16.3-a3 |
16.3-a |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$612.2234929$ |
1.507811580 |
\( -164286883 a^{3} + 50566227 a^{2} + 1235508110 a + 776641025 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( 0\) , \( \frac{3}{2} a^{3} + \frac{1}{2} a^{2} - 6 a - 2\) , \( a^{2} + 6 a + 2\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}^{2}+\left(\frac{3}{2}a^{3}+\frac{1}{2}a^{2}-6a-2\right){x}+a^{2}+6a+2$ |
| 16.3-a4 |
16.3-a |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$306.1117464$ |
1.507811580 |
\( \frac{2142331909}{2} a^{3} + 1243135217 a^{2} - \frac{7138461435}{2} a - 2711405361 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( -\frac{7}{2} a^{3} + \frac{17}{2} a^{2} + 4 a - 3\) , \( -\frac{11}{2} a^{3} + 4 a^{2} + \frac{65}{2} a + 16\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{7}{2}a+2\right){x}^{2}+\left(-\frac{7}{2}a^{3}+\frac{17}{2}a^{2}+4a-3\right){x}-\frac{11}{2}a^{3}+4a^{2}+\frac{65}{2}a+16$ |
| 16.3-a5 |
16.3-a |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$76.52793662$ |
1.507811580 |
\( \frac{728135853331382213}{2} a^{3} - 980179099591901196 a^{2} - \frac{3739800265535979205}{2} a + 4207070245068800873 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( 113 a^{3} - 78 a^{2} - 746 a - 444\) , \( \frac{1527}{2} a^{3} + \frac{43}{2} a^{2} - 6377 a - 4174\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}-a{x}^{2}+\left(113a^{3}-78a^{2}-746a-444\right){x}+\frac{1527}{2}a^{3}+\frac{43}{2}a^{2}-6377a-4174$ |
| 16.3-a6 |
16.3-a |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$612.2234929$ |
1.507811580 |
\( 164286883 a^{3} - 442294422 a^{2} - 843779915 a + 1898428479 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( 48 a^{3} - 18 a^{2} - 356 a - 224\) , \( -437 a^{3} + 131 a^{2} + 3293 a + 2070\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}-a{x}^{2}+\left(48a^{3}-18a^{2}-356a-224\right){x}-437a^{3}+131a^{2}+3293a+2070$ |
| 16.3-b1 |
16.3-b |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$19.13198415$ |
0.753905790 |
\( -\frac{728135853331382213}{2} a^{3} + \frac{224049360810344247}{2} a^{2} + 2738054551954718675 a + 1721058939374601181 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( 41 a^{3} - 170 a^{2} + 86 a + 142\) , \( 3971 a^{3} - 16520 a^{2} + 7899 a + 14698\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){x}^{2}+\left(41a^{3}-170a^{2}+86a+142\right){x}+3971a^{3}-16520a^{2}+7899a+14698$ |
| 16.3-b2 |
16.3-b |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$612.2234929$ |
0.753905790 |
\( \frac{728135853331382213}{2} a^{3} - 980179099591901196 a^{2} - \frac{3739800265535979205}{2} a + 4207070245068800873 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{7}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( -28 a^{3} + \frac{141}{2} a^{2} + \frac{287}{2} a - 304\) , \( 165 a^{3} - 423 a^{2} - 838 a + 1829\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{7}{2}a+2\right){x}^{2}+\left(-28a^{3}+\frac{141}{2}a^{2}+\frac{287}{2}a-304\right){x}+165a^{3}-423a^{2}-838a+1829$ |
| 16.3-b3 |
16.3-b |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$1224.446985$ |
0.753905790 |
\( 164286883 a^{3} - 442294422 a^{2} - 843779915 a + 1898428479 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{7}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( -3 a^{3} + \frac{1}{2} a^{2} + \frac{27}{2} a - 4\) , \( \frac{5}{2} a^{3} + \frac{1}{2} a^{2} - 10 a + 1\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{7}{2}a+2\right){x}^{2}+\left(-3a^{3}+\frac{1}{2}a^{2}+\frac{27}{2}a-4\right){x}+\frac{5}{2}a^{3}+\frac{1}{2}a^{2}-10a+1$ |
| 16.3-b4 |
16.3-b |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$76.52793662$ |
0.753905790 |
\( -\frac{2142331909}{2} a^{3} + \frac{8913266161}{2} a^{2} - 2130537580 a - 3966334907 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 4\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( 7 a^{3} - \frac{45}{2} a^{2} - \frac{1}{2} a + 26\) , \( \frac{43}{2} a^{3} - \frac{163}{2} a^{2} + 30 a + 71\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+4\right){x}^{2}+\left(7a^{3}-\frac{45}{2}a^{2}-\frac{1}{2}a+26\right){x}+\frac{43}{2}a^{3}-\frac{163}{2}a^{2}+30a+71$ |
| 16.3-b5 |
16.3-b |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$612.2234929$ |
0.753905790 |
\( \frac{2142331909}{2} a^{3} + 1243135217 a^{2} - \frac{7138461435}{2} a - 2711405361 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( -a^{3} + \frac{3}{2} a^{2} + \frac{7}{2} a - 2\) , \( 31 a^{3} - 9 a^{2} - 236 a - 151\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}^{2}+\left(-a^{3}+\frac{3}{2}a^{2}+\frac{7}{2}a-2\right){x}+31a^{3}-9a^{2}-236a-151$ |
| 16.3-b6 |
16.3-b |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$306.1117464$ |
0.753905790 |
\( -164286883 a^{3} + 50566227 a^{2} + 1235508110 a + 776641025 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 2\) , \( 0\) , \( -156 a^{3} + \frac{777}{2} a^{2} + \frac{1569}{2} a - 1684\) , \( 2203 a^{3} - 6023 a^{2} - 11359 a + 25795\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a+2\right){x}^{2}+\left(-156a^{3}+\frac{777}{2}a^{2}+\frac{1569}{2}a-1684\right){x}+2203a^{3}-6023a^{2}-11359a+25795$ |
| 16.3-c1 |
16.3-c |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{8} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.467342284$ |
$458.6811557$ |
3.315197531 |
\( 17715448725492 a^{3} - 47695255552025 a^{2} - 90988843777996 a + 204714926129964 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -5 a^{3} + 17 a^{2} - 23\) , \( -\frac{7}{2} a^{3} + \frac{29}{2} a^{2} - 12 a - 4\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a\right){x}^{2}+\left(-5a^{3}+17a^{2}-23\right){x}-\frac{7}{2}a^{3}+\frac{29}{2}a^{2}-12a-4$ |
| 16.3-c2 |
16.3-c |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{10} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.733671142$ |
$229.3405778$ |
3.315197531 |
\( -3502882815 a^{3} + 14199881717 a^{2} - 6044041225 a - 12152175830 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a + 2\) , \( 0\) , \( 20 a^{3} + 20 a^{2} - 76 a - 56\) , \( 57 a^{3} + 48 a^{2} - 242 a - 172\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{7}{2}a+2\right){x}^{2}+\left(20a^{3}+20a^{2}-76a-56\right){x}+57a^{3}+48a^{2}-242a-172$ |
| 16.3-c3 |
16.3-c |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{8} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.366835571$ |
$1834.724623$ |
3.315197531 |
\( -12990 a^{3} + 44327 a^{2} - 2612 a - 22636 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a + 2\) , \( 0\) , \( -5 a^{3} - 5 a^{2} + 19 a + 14\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{7}{2}a+2\right){x}^{2}+\left(-5a^{3}-5a^{2}+19a+14\right){x}$ |
| 16.3-c4 |
16.3-c |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{4} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$0.733671142$ |
$1834.724623$ |
3.315197531 |
\( 1151010 a^{3} - 3079137 a^{2} - 5902248 a + 13230920 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( -\frac{3}{2} a^{3} + 5 a^{2} + \frac{15}{2} a - 22\) , \( \frac{5}{2} a^{3} - 6 a^{2} - \frac{25}{2} a + 26\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-2\right){x}^{2}+\left(-\frac{3}{2}a^{3}+5a^{2}+\frac{15}{2}a-22\right){x}+\frac{5}{2}a^{3}-6a^{2}-\frac{25}{2}a+26$ |
| 16.3-c5 |
16.3-c |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{10} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.183417785$ |
$917.3623115$ |
3.315197531 |
\( 18075 a^{3} + 20807 a^{2} - 60279 a - 45178 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( a^{3} - \frac{13}{2} a^{2} - \frac{9}{2} a + 31\) , \( \frac{17}{2} a^{3} - \frac{49}{2} a^{2} - 42 a + 109\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a+2\right){x}^{2}+\left(a^{3}-\frac{13}{2}a^{2}-\frac{9}{2}a+31\right){x}+\frac{17}{2}a^{3}-\frac{49}{2}a^{2}-42a+109$ |
| 16.3-c6 |
16.3-c |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{8} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1.467342284$ |
$229.3405778$ |
3.315197531 |
\( 812929248 a^{3} + 943476501 a^{2} - 2708809800 a - 2057759320 \) |
\( \bigl[a\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{5}{2} a + 2\) , \( 0\) , \( 29 a^{3} - 125 a^{2} + 68 a + 120\) , \( 334 a^{3} - 1392 a^{2} + 670 a + 1243\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{5}{2}a+2\right){x}^{2}+\left(29a^{3}-125a^{2}+68a+120\right){x}+334a^{3}-1392a^{2}+670a+1243$ |
| 16.3-d1 |
16.3-d |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{10} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.313326990$ |
$1163.366282$ |
1.795483256 |
\( 18075 a^{3} + 20807 a^{2} - 60279 a - 45178 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 5 a + 8\) , \( -33 a^{3} + 11 a^{2} + 248 a + 152\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}^{2}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+5a+8\right){x}-33a^{3}+11a^{2}+248a+152$ |
| 16.3-d2 |
16.3-d |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{8} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$2.506615925$ |
$36.35519632$ |
1.795483256 |
\( 17715448725492 a^{3} - 47695255552025 a^{2} - 90988843777996 a + 204714926129964 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( 5 a^{3} - \frac{1}{2} a^{2} - \frac{73}{2} a - 25\) , \( \frac{11}{2} a^{3} - 11 a^{2} - \frac{141}{2} a - 46\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+1\right){x}^{2}+\left(5a^{3}-\frac{1}{2}a^{2}-\frac{73}{2}a-25\right){x}+\frac{11}{2}a^{3}-11a^{2}-\frac{141}{2}a-46$ |
| 16.3-d3 |
16.3-d |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{4} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1.253307962$ |
$581.6831411$ |
1.795483256 |
\( 1151010 a^{3} - 3079137 a^{2} - 5902248 a + 13230920 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{2} - \frac{3}{2} a\) , \( -6 a^{3} - 7 a^{2} + 20 a + 15\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+1\right){x}^{2}+\left(-\frac{1}{2}a^{2}-\frac{3}{2}a\right){x}-6a^{3}-7a^{2}+20a+15$ |
| 16.3-d4 |
16.3-d |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{10} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.253307962$ |
$1163.366282$ |
1.795483256 |
\( -3502882815 a^{3} + 14199881717 a^{2} - 6044041225 a - 12152175830 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( -\frac{17}{2} a^{3} + \frac{39}{2} a^{2} + 45 a - 82\) , \( 25 a^{3} - 69 a^{2} - 129 a + 298\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{7}{2}a+1\right){x}^{2}+\left(-\frac{17}{2}a^{3}+\frac{39}{2}a^{2}+45a-82\right){x}+25a^{3}-69a^{2}-129a+298$ |
| 16.3-d5 |
16.3-d |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{8} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.626653981$ |
$2326.732564$ |
1.795483256 |
\( -12990 a^{3} + 44327 a^{2} - 2612 a - 22636 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( -\frac{7}{2} a^{3} + \frac{9}{2} a^{2} + 20 a - 12\) , \( -\frac{7}{2} a^{3} + \frac{11}{2} a^{2} + 20 a - 18\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{7}{2}a+1\right){x}^{2}+\left(-\frac{7}{2}a^{3}+\frac{9}{2}a^{2}+20a-12\right){x}-\frac{7}{2}a^{3}+\frac{11}{2}a^{2}+20a-18$ |
| 16.3-d6 |
16.3-d |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{8} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$2.506615925$ |
$72.71039264$ |
1.795483256 |
\( 812929248 a^{3} + 943476501 a^{2} - 2708809800 a - 2057759320 \) |
\( \bigl[a\) , \( -a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( -88 a^{3} + 236 a^{2} + 451 a - 1010\) , \( -1459 a^{3} + 3928 a^{2} + 7493 a - 16860\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){y}={x}^{3}-a{x}^{2}+\left(-88a^{3}+236a^{2}+451a-1010\right){x}-1459a^{3}+3928a^{2}+7493a-16860$ |
*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.
