| 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 |
| 26411.1-a1 |
26411.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
26411.1 |
\( 7^{4} \cdot 11 \) |
\( 7^{18} \cdot 11^{4} \) |
$3.77817$ |
$(-2a+1), (7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.254267011$ |
$0.339349799$ |
4.106683497 |
\( \frac{4657463}{41503} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 170\) , \( -3237\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+170{x}-3237$ |
| 26411.1-a2 |
26411.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
26411.1 |
\( 7^{4} \cdot 11 \) |
\( 7^{24} \cdot 11^{2} \) |
$3.77817$ |
$(-2a+1), (7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.017068046$ |
$0.169674899$ |
4.106683497 |
\( \frac{15124197817}{1294139} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2525\) , \( -45279\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2525{x}-45279$ |
| 26411.1-b1 |
26411.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
26411.1 |
\( 7^{4} \cdot 11 \) |
\( 7^{16} \cdot 11^{2} \) |
$3.77817$ |
$(-2a+1), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cn, 3B |
$1$ |
\( 2^{3} \) |
$0.380901696$ |
$0.257712460$ |
0.947113353 |
\( -\frac{78843215872}{539} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -4377\) , \( -110013\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-4377{x}-110013$ |
| 26411.1-b2 |
26411.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
26411.1 |
\( 7^{4} \cdot 11 \) |
\( 7^{24} \cdot 11^{6} \) |
$3.77817$ |
$(-2a+1), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cn, 3Cs |
$1$ |
\( 2^{3} \) |
$1.142705089$ |
$0.085904153$ |
0.947113353 |
\( -\frac{13278380032}{156590819} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -2417\) , \( -210708\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-2417{x}-210708$ |
| 26411.1-b3 |
26411.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
26411.1 |
\( 7^{4} \cdot 11 \) |
\( 7^{16} \cdot 11^{18} \) |
$3.77817$ |
$(-2a+1), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cn, 3B |
$1$ |
\( 2^{3} \) |
$3.428115269$ |
$0.028634717$ |
0.947113353 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 21593\) , \( 5467657\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+21593{x}+5467657$ |
| 26411.1-c1 |
26411.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
26411.1 |
\( 7^{4} \cdot 11 \) |
\( 7^{12} \cdot 11^{2} \) |
$3.77817$ |
$(-2a+1), (7)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2Cn, 5B.4.2 |
$1$ |
\( 2^{3} \) |
$9.796079568$ |
$0.052901246$ |
10.00004236 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -383196\) , \( 91174234\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-383196{x}+91174234$ |
| 26411.1-c2 |
26411.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
26411.1 |
\( 7^{4} \cdot 11 \) |
\( 7^{12} \cdot 11^{10} \) |
$3.77817$ |
$(-2a+1), (7)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2Cn, 5Cs.4.1 |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.391843182$ |
$0.264506231$ |
10.00004236 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -506\) , \( 7774\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-506{x}+7774$ |
| 26411.1-c3 |
26411.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
26411.1 |
\( 7^{4} \cdot 11 \) |
\( 7^{12} \cdot 11^{2} \) |
$3.77817$ |
$(-2a+1), (7)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2Cn, 5B.4.1 |
$1$ |
\( 2^{3} \) |
$0.391843182$ |
$1.322531159$ |
10.00004236 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -16\) , \( -66\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-16{x}-66$ |
| 26411.1-d1 |
26411.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
26411.1 |
\( 7^{4} \cdot 11 \) |
\( 7^{16} \cdot 11^{2} \) |
$3.77817$ |
$(-2a+1), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cn |
$1$ |
\( 2^{3} \) |
$1.959156042$ |
$0.688939123$ |
13.02277425 |
\( \frac{884736}{539} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 98\) , \( -86\bigr] \) |
${y}^2+{y}={x}^{3}+98{x}-86$ |
*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.
