| 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 |
| 2601.5-a1 |
2601.5-a |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2601.5 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{10} \cdot 17^{4} \) |
$1.80496$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3^{3} \) |
$0.018964757$ |
$2.164363860$ |
1.567315135 |
\( \frac{14811123712}{96702579} a + \frac{26737709056}{96702579} \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( 3 a - 5\) , \( -2 a + 10\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(3a-5\right){x}-2a+10$ |
| 2601.5-b1 |
2601.5-b |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2601.5 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{10} \cdot 17^{4} \) |
$1.80496$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3^{3} \) |
$0.018964757$ |
$2.164363860$ |
1.567315135 |
\( -\frac{14811123712}{96702579} a + \frac{26737709056}{96702579} \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( -3 a - 5\) , \( a + 10\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-3a-5\right){x}+a+10$ |
| 2601.5-c1 |
2601.5-c |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2601.5 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{2} \cdot 17^{6} \) |
$1.80496$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1.351542505$ |
$1.679417732$ |
3.209988236 |
\( -\frac{23100424192}{14739} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -59\) , \( -196\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-59{x}-196$ |
| 2601.5-c2 |
2601.5-c |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2601.5 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{6} \cdot 17^{2} \) |
$1.80496$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$0.450514168$ |
$5.038253197$ |
3.209988236 |
\( \frac{32768}{459} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( -1\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+{x}-1$ |
| 2601.5-d1 |
2601.5-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2601.5 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{16} \cdot 17^{4} \) |
$1.80496$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.443141991$ |
1.880092244 |
\( -\frac{372082589114986904}{2610969633} a - \frac{181318779827784209}{2610969633} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 1087 a + 92\) , \( -10290 a - 17475\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1087a+92\right){x}-10290a-17475$ |
| 2601.5-d2 |
2601.5-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2601.5 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{8} \cdot 17^{8} \) |
$1.80496$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.886283983$ |
1.880092244 |
\( \frac{147770521717808}{17596287801} a - \frac{136210703475223}{17596287801} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 67 a + 7\) , \( -158 a - 254\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(67a+7\right){x}-158a-254$ |
| 2601.5-d3 |
2601.5-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2601.5 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{4} \cdot 17^{13} \) |
$1.80496$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$0.443141991$ |
1.880092244 |
\( \frac{1695948356939509768}{15730800405203547} a - \frac{7330062339265374821}{15730800405203547} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 7 a - 158\) , \( -2 a - 1661\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(7a-158\right){x}-2a-1661$ |
| 2601.5-d4 |
2601.5-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2601.5 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{4} \cdot 17^{7} \) |
$1.80496$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.772567966$ |
1.880092244 |
\( -\frac{3780522976}{2255067} a + \frac{417620747}{2255067} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 7 a + 12\) , \( -14 a + 23\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(7a+12\right){x}-14a+23$ |
| 2601.5-e1 |
2601.5-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2601.5 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{16} \cdot 17^{4} \) |
$1.80496$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.443141991$ |
1.880092244 |
\( \frac{372082589114986904}{2610969633} a - \frac{181318779827784209}{2610969633} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -1087 a + 92\) , \( 10290 a - 17475\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-1087a+92\right){x}+10290a-17475$ |
| 2601.5-e2 |
2601.5-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2601.5 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{8} \cdot 17^{8} \) |
$1.80496$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.886283983$ |
1.880092244 |
\( -\frac{147770521717808}{17596287801} a - \frac{136210703475223}{17596287801} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -67 a + 7\) , \( 158 a - 254\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-67a+7\right){x}+158a-254$ |
| 2601.5-e3 |
2601.5-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2601.5 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{4} \cdot 17^{13} \) |
$1.80496$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$0.443141991$ |
1.880092244 |
\( -\frac{1695948356939509768}{15730800405203547} a - \frac{7330062339265374821}{15730800405203547} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -7 a - 158\) , \( 2 a - 1661\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-7a-158\right){x}+2a-1661$ |
| 2601.5-e4 |
2601.5-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2601.5 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{4} \cdot 17^{7} \) |
$1.80496$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.772567966$ |
1.880092244 |
\( \frac{3780522976}{2255067} a + \frac{417620747}{2255067} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -7 a + 12\) , \( 14 a + 23\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-7a+12\right){x}+14a+23$ |
*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.
