| 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 |
| 25.1-a1 |
25.1-a |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.157899867$ |
$578.9290819$ |
2.756200396 |
\( \frac{10926784}{25} a^{3} - \frac{47031648}{25} a^{2} - \frac{20178048}{5} a + \frac{434524288}{25} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{2} - a - 5\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 3\) , \( -\frac{83}{2} a^{3} - \frac{241}{2} a^{2} + 200 a + 573\) , \( \frac{837}{2} a^{3} + 1278 a^{2} - 1993 a - 6092\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-a-5\right){x}^{2}+\left(-\frac{83}{2}a^{3}-\frac{241}{2}a^{2}+200a+573\right){x}+\frac{837}{2}a^{3}+1278a^{2}-1993a-6092$ |
| 25.1-a2 |
25.1-a |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$0.078949933$ |
$578.9290819$ |
2.756200396 |
\( -\frac{4420288383104}{5} a^{3} - 1929582615456 a^{2} + 8165216797056 a + \frac{89108781027392}{5} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( -\frac{1}{2} a^{3} + 4 a + 1\) , \( \frac{1}{2} a^{2} - 4\) , \( -2 a^{3} + \frac{23}{2} a^{2} + 6 a - 60\) , \( -6 a^{3} + \frac{37}{2} a^{2} + 30 a - 86\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{2}a^{2}-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+4a+1\right){x}^{2}+\left(-2a^{3}+\frac{23}{2}a^{2}+6a-60\right){x}-6a^{3}+\frac{37}{2}a^{2}+30a-86$ |
| 25.1-b1 |
25.1-b |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.333998981$ |
$958.2743538$ |
4.825126117 |
\( \frac{314304}{5} a^{3} - \frac{671584}{5} a^{2} - 587136 a + \frac{6359936}{5} \) |
\( \bigl[\frac{1}{2} a^{3} - 4 a\) , \( \frac{1}{2} a^{2} + a - 4\) , \( \frac{1}{2} a^{2} + a - 3\) , \( a^{3} - 8 a - 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a - 3\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-4a\right){x}{y}+\left(\frac{1}{2}a^{2}+a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}+a-4\right){x}^{2}+\left(a^{3}-8a-2\right){x}-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a-3$ |
| 25.1-b2 |
25.1-b |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.166999490$ |
$958.2743538$ |
4.825126117 |
\( -\frac{470666496}{5} a^{3} + \frac{1430403296}{5} a^{2} + \frac{2242224512}{5} a - \frac{6814343872}{5} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{2} + a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 4 a - 4\) , \( -8 a^{3} - \frac{47}{2} a^{2} + 38 a + 112\) , \( 15 a^{3} + \frac{93}{2} a^{2} - 72 a - 224\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-4a-4\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}+a-3\right){x}^{2}+\left(-8a^{3}-\frac{47}{2}a^{2}+38a+112\right){x}+15a^{3}+\frac{93}{2}a^{2}-72a-224$ |
| 25.1-c1 |
25.1-c |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$0.053421033$ |
$474.4234320$ |
3.056624322 |
\( \frac{210432}{25} a^{3} - \frac{522144}{25} a^{2} - \frac{1653632}{25} a + 159040 \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a - 3\) , \( \frac{1}{2} a^{2} - 4\) , \( -\frac{11}{2} a^{3} + 14 a^{2} + 43 a - 104\) , \( -13 a^{3} + \frac{61}{2} a^{2} + 111 a - 253\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{2}a^{2}-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a-3\right){x}^{2}+\left(-\frac{11}{2}a^{3}+14a^{2}+43a-104\right){x}-13a^{3}+\frac{61}{2}a^{2}+111a-253$ |
| 25.1-c2 |
25.1-c |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.106842066$ |
$1897.693728$ |
3.056624322 |
\( -\frac{897433536}{5} a^{3} + \frac{2727334176}{5} a^{2} + 855070592 a - 2598547328 \) |
\( \bigl[a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 4 a + 3\) , \( \frac{1}{2} a^{2} + a - 3\) , \( -\frac{1}{2} a^{3} - \frac{3}{2} a^{2} + a + 2\) , \( -\frac{1}{2} a^{3} - a^{2} + 3 a + 4\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{2}+a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+4a+3\right){x}^{2}+\left(-\frac{1}{2}a^{3}-\frac{3}{2}a^{2}+a+2\right){x}-\frac{1}{2}a^{3}-a^{2}+3a+4$ |
| 25.1-d1 |
25.1-d |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.077547899$ |
$1658.434311$ |
3.877680038 |
\( \frac{379008}{5} a^{2} - \frac{1804736}{5} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{2} - a - 5\) , \( a + 1\) , \( -a^{3} - \frac{3}{2} a^{2} + 7 a + 13\) , \( \frac{1}{2} a^{2} - a - 5\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-a-5\right){x}^{2}+\left(-a^{3}-\frac{3}{2}a^{2}+7a+13\right){x}+\frac{1}{2}a^{2}-a-5$ |
| 25.1-d2 |
25.1-d |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.155095799$ |
$1658.434311$ |
3.877680038 |
\( -2176 a^{2} + \frac{99904}{5} \) |
\( \bigl[a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 3 a + 4\) , \( \frac{1}{2} a^{3} - 4 a + 1\) , \( -a^{3} - \frac{1}{2} a^{2} + 6 a + 8\) , \( \frac{9}{2} a^{2} + 2 a - 25\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{3}-4a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+3a+4\right){x}^{2}+\left(-a^{3}-\frac{1}{2}a^{2}+6a+8\right){x}+\frac{9}{2}a^{2}+2a-25$ |
| 25.1-e1 |
25.1-e |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$0.539021742$ |
$155.3309810$ |
5.048914569 |
\( \frac{4420288383104}{5} a^{3} - 1929582615456 a^{2} - 8165216797056 a + \frac{89108781027392}{5} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( -\frac{1}{2} a^{3} + 3 a - 1\) , \( \frac{1}{2} a^{2} + a - 4\) , \( -36 a^{3} + \frac{215}{2} a^{2} + 171 a - 511\) , \( -\frac{2629}{2} a^{3} + 3994 a^{2} + 6263 a - 19029\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{2}a^{2}+a-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+3a-1\right){x}^{2}+\left(-36a^{3}+\frac{215}{2}a^{2}+171a-511\right){x}-\frac{2629}{2}a^{3}+3994a^{2}+6263a-19029$ |
| 25.1-e2 |
25.1-e |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.269510871$ |
$621.3239243$ |
5.048914569 |
\( -\frac{10926784}{25} a^{3} - \frac{47031648}{25} a^{2} + \frac{20178048}{5} a + \frac{434524288}{25} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 5 a + 3\) , \( \frac{1}{2} a^{2} - 3\) , \( -\frac{3}{2} a^{3} - 2 a^{2} + 8 a + 14\) , \( -3 a^{3} + \frac{3}{2} a^{2} + 22 a - 27\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{2}a^{2}-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-5a+3\right){x}^{2}+\left(-\frac{3}{2}a^{3}-2a^{2}+8a+14\right){x}-3a^{3}+\frac{3}{2}a^{2}+22a-27$ |
| 25.1-f1 |
25.1-f |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.065530087$ |
$1653.870785$ |
3.267728633 |
\( \frac{470666496}{5} a^{3} + \frac{1430403296}{5} a^{2} - \frac{2242224512}{5} a - \frac{6814343872}{5} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 4\) , \( \frac{1}{2} a^{2} - 4\) , \( 2 a^{3} - \frac{5}{2} a^{2} - 18 a + 30\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + 5 a - 16\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{2}a^{2}-4\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a+4\right){x}^{2}+\left(2a^{3}-\frac{5}{2}a^{2}-18a+30\right){x}-\frac{1}{2}a^{3}+2a^{2}+5a-16$ |
| 25.1-f2 |
25.1-f |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.131060175$ |
$1653.870785$ |
3.267728633 |
\( -\frac{314304}{5} a^{3} - \frac{671584}{5} a^{2} + 587136 a + \frac{6359936}{5} \) |
\( \bigl[a\) , \( -\frac{1}{2} a^{2} + a + 4\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 3\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - 12 a - 13\) , \( -\frac{3}{2} a^{3} - \frac{5}{2} a^{2} + 21 a + 42\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+a+4\right){x}^{2}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-12a-13\right){x}-\frac{3}{2}a^{3}-\frac{5}{2}a^{2}+21a+42$ |
| 25.1-g1 |
25.1-g |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.135962750$ |
$1052.818947$ |
4.315958800 |
\( -\frac{210432}{25} a^{3} - \frac{522144}{25} a^{2} + \frac{1653632}{25} a + 159040 \) |
\( \bigl[\frac{1}{2} a^{3} - 4 a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 5 a - 5\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 4\) , \( -a^{3} + \frac{1}{2} a^{2} + 8 a - 6\) , \( -\frac{1}{2} a^{3} + a^{2} + 4 a - 15\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-4a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-4\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-5a-5\right){x}^{2}+\left(-a^{3}+\frac{1}{2}a^{2}+8a-6\right){x}-\frac{1}{2}a^{3}+a^{2}+4a-15$ |
| 25.1-g2 |
25.1-g |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$0.067981375$ |
$1052.818947$ |
4.315958800 |
\( \frac{897433536}{5} a^{3} + \frac{2727334176}{5} a^{2} - 855070592 a - 2598547328 \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( -a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 4 a - 3\) , \( 3 a^{3} + 12 a^{2} - 35 a - 100\) , \( 2 a^{3} + \frac{23}{2} a^{2} - 25 a - 89\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-4a-3\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(3a^{3}+12a^{2}-35a-100\right){x}+2a^{3}+\frac{23}{2}a^{2}-25a-89$ |
| 25.1-h1 |
25.1-h |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$0.053421033$ |
$474.4234320$ |
3.056624322 |
\( -\frac{210432}{25} a^{3} - \frac{522144}{25} a^{2} + \frac{1653632}{25} a + 159040 \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 3\) , \( \frac{1}{2} a^{2} - 4\) , \( \frac{11}{2} a^{3} + 14 a^{2} - 44 a - 104\) , \( 13 a^{3} + \frac{61}{2} a^{2} - 111 a - 253\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{2}a^{2}-4\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-3\right){x}^{2}+\left(\frac{11}{2}a^{3}+14a^{2}-44a-104\right){x}+13a^{3}+\frac{61}{2}a^{2}-111a-253$ |
| 25.1-h2 |
25.1-h |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.106842066$ |
$1897.693728$ |
3.056624322 |
\( \frac{897433536}{5} a^{3} + \frac{2727334176}{5} a^{2} - 855070592 a - 2598547328 \) |
\( \bigl[a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 3\) , \( \frac{1}{2} a^{2} + a - 3\) , \( -\frac{3}{2} a^{2} + 2 a + 2\) , \( -a^{2} + 4\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{2}+a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a+3\right){x}^{2}+\left(-\frac{3}{2}a^{2}+2a+2\right){x}-a^{2}+4$ |
| 25.1-i1 |
25.1-i |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.333998981$ |
$958.2743538$ |
4.825126117 |
\( -\frac{314304}{5} a^{3} - \frac{671584}{5} a^{2} + 587136 a + \frac{6359936}{5} \) |
\( \bigl[\frac{1}{2} a^{3} - 4 a\) , \( \frac{1}{2} a^{2} - a - 4\) , \( \frac{1}{2} a^{2} + a - 3\) , \( -a^{3} + 7 a - 2\) , \( \frac{1}{2} a^{2} - 3\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-4a\right){x}{y}+\left(\frac{1}{2}a^{2}+a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-a-4\right){x}^{2}+\left(-a^{3}+7a-2\right){x}+\frac{1}{2}a^{2}-3$ |
| 25.1-i2 |
25.1-i |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.166999490$ |
$958.2743538$ |
4.825126117 |
\( \frac{470666496}{5} a^{3} + \frac{1430403296}{5} a^{2} - \frac{2242224512}{5} a - \frac{6814343872}{5} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{2} - a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 4 a - 4\) , \( 8 a^{3} - \frac{47}{2} a^{2} - 39 a + 112\) , \( -\frac{29}{2} a^{3} + \frac{93}{2} a^{2} + 67 a - 224\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-4a-4\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-a-3\right){x}^{2}+\left(8a^{3}-\frac{47}{2}a^{2}-39a+112\right){x}-\frac{29}{2}a^{3}+\frac{93}{2}a^{2}+67a-224$ |
| 25.1-j1 |
25.1-j |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.157899867$ |
$578.9290819$ |
2.756200396 |
\( -\frac{10926784}{25} a^{3} - \frac{47031648}{25} a^{2} + \frac{20178048}{5} a + \frac{434524288}{25} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{2} + a - 5\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 3\) , \( 41 a^{3} - \frac{241}{2} a^{2} - 198 a + 573\) , \( -419 a^{3} + 1278 a^{2} + 1995 a - 6092\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}+a-5\right){x}^{2}+\left(41a^{3}-\frac{241}{2}a^{2}-198a+573\right){x}-419a^{3}+1278a^{2}+1995a-6092$ |
| 25.1-j2 |
25.1-j |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$0.078949933$ |
$578.9290819$ |
2.756200396 |
\( \frac{4420288383104}{5} a^{3} - 1929582615456 a^{2} - 8165216797056 a + \frac{89108781027392}{5} \) |
\( \bigl[a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 3 a + 5\) , \( \frac{1}{2} a^{2} - 4\) , \( -8 a^{3} + \frac{35}{2} a^{2} + 72 a - 147\) , \( 25 a^{3} - \frac{113}{2} a^{2} - 235 a + 526\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{2}-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+3a+5\right){x}^{2}+\left(-8a^{3}+\frac{35}{2}a^{2}+72a-147\right){x}+25a^{3}-\frac{113}{2}a^{2}-235a+526$ |
| 25.1-k1 |
25.1-k |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.077547899$ |
$1658.434311$ |
3.877680038 |
\( \frac{379008}{5} a^{2} - \frac{1804736}{5} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{2} + a - 5\) , \( a + 1\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - 4 a + 13\) , \( \frac{1}{2} a^{2} - 5\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}+a-5\right){x}^{2}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-4a+13\right){x}+\frac{1}{2}a^{2}-5$ |
| 25.1-k2 |
25.1-k |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.155095799$ |
$1658.434311$ |
3.877680038 |
\( -2176 a^{2} + \frac{99904}{5} \) |
\( \bigl[a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 4\) , \( \frac{1}{2} a^{3} - 4 a + 1\) , \( a^{3} - \frac{1}{2} a^{2} - 7 a + 8\) , \( -\frac{1}{2} a^{3} + \frac{9}{2} a^{2} + 2 a - 25\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{3}-4a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+4\right){x}^{2}+\left(a^{3}-\frac{1}{2}a^{2}-7a+8\right){x}-\frac{1}{2}a^{3}+\frac{9}{2}a^{2}+2a-25$ |
| 25.1-l1 |
25.1-l |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.135962750$ |
$1052.818947$ |
4.315958800 |
\( \frac{210432}{25} a^{3} - \frac{522144}{25} a^{2} - \frac{1653632}{25} a + 159040 \) |
\( \bigl[\frac{1}{2} a^{3} - 4 a\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 5 a - 5\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 4\) , \( \frac{3}{2} a^{3} + \frac{1}{2} a^{2} - 13 a - 6\) , \( \frac{1}{2} a^{3} + a^{2} - 5 a - 15\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-4a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+5a-5\right){x}^{2}+\left(\frac{3}{2}a^{3}+\frac{1}{2}a^{2}-13a-6\right){x}+\frac{1}{2}a^{3}+a^{2}-5a-15$ |
| 25.1-l2 |
25.1-l |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$0.067981375$ |
$1052.818947$ |
4.315958800 |
\( -\frac{897433536}{5} a^{3} + \frac{2727334176}{5} a^{2} + 855070592 a - 2598547328 \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 4 a - 3\) , \( -\frac{7}{2} a^{3} + 12 a^{2} + 37 a - 100\) , \( -2 a^{3} + \frac{23}{2} a^{2} + 24 a - 89\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-4a-3\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-\frac{7}{2}a^{3}+12a^{2}+37a-100\right){x}-2a^{3}+\frac{23}{2}a^{2}+24a-89$ |
| 25.1-m1 |
25.1-m |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.065530087$ |
$1653.870785$ |
3.267728633 |
\( -\frac{470666496}{5} a^{3} + \frac{1430403296}{5} a^{2} + \frac{2242224512}{5} a - \frac{6814343872}{5} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 4 a + 4\) , \( \frac{1}{2} a^{2} - 4\) , \( -2 a^{3} - \frac{5}{2} a^{2} + 17 a + 30\) , \( \frac{1}{2} a^{3} + 2 a^{2} - 5 a - 16\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{2}a^{2}-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+4a+4\right){x}^{2}+\left(-2a^{3}-\frac{5}{2}a^{2}+17a+30\right){x}+\frac{1}{2}a^{3}+2a^{2}-5a-16$ |
| 25.1-m2 |
25.1-m |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.131060175$ |
$1653.870785$ |
3.267728633 |
\( \frac{314304}{5} a^{3} - \frac{671584}{5} a^{2} - 587136 a + \frac{6359936}{5} \) |
\( \bigl[a\) , \( -\frac{1}{2} a^{2} - a + 4\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 3\) , \( -a^{3} - \frac{3}{2} a^{2} + 15 a - 13\) , \( a^{3} - \frac{5}{2} a^{2} - 19 a + 42\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}-a+4\right){x}^{2}+\left(-a^{3}-\frac{3}{2}a^{2}+15a-13\right){x}+a^{3}-\frac{5}{2}a^{2}-19a+42$ |
| 25.1-n1 |
25.1-n |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.269510871$ |
$621.3239243$ |
5.048914569 |
\( \frac{10926784}{25} a^{3} - \frac{47031648}{25} a^{2} - \frac{20178048}{5} a + \frac{434524288}{25} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 5 a + 3\) , \( \frac{1}{2} a^{2} - 3\) , \( a^{3} - 2 a^{2} - 6 a + 14\) , \( 3 a^{3} + \frac{3}{2} a^{2} - 22 a - 27\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{2}a^{2}-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+5a+3\right){x}^{2}+\left(a^{3}-2a^{2}-6a+14\right){x}+3a^{3}+\frac{3}{2}a^{2}-22a-27$ |
| 25.1-n2 |
25.1-n |
$2$ |
$2$ |
4.4.17600.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$17.72709$ |
$(a^2-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$0.539021742$ |
$155.3309810$ |
5.048914569 |
\( -\frac{4420288383104}{5} a^{3} - 1929582615456 a^{2} + 8165216797056 a + \frac{89108781027392}{5} \) |
\( \bigl[a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 4 a - 5\) , \( \frac{1}{2} a^{2} + a - 4\) , \( 5 a^{3} + 16 a^{2} - 23 a - 81\) , \( 73 a^{3} + \frac{445}{2} a^{2} - 347 a - 1062\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{2}+a-4\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-4a-5\right){x}^{2}+\left(5a^{3}+16a^{2}-23a-81\right){x}+73a^{3}+\frac{445}{2}a^{2}-347a-1062$ |
*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.
