| 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 |
| 539.1-b3 |
539.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
539.1 |
\( 7^{2} \cdot 11 \) |
\( 7^{4} \cdot 11^{18} \) |
$1.42801$ |
$(-2a+1), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cn, 3B.1.2 |
$4$ |
\( 2^{2} \) |
$1$ |
$0.200443024$ |
1.933947068 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+441{x}-15815$ |
| 13475.1-b3 |
13475.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
13475.1 |
\( 5^{2} \cdot 7^{2} \cdot 11 \) |
\( 5^{6} \cdot 7^{4} \cdot 11^{18} \) |
$3.19313$ |
$(-a-1), (-2a+1), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.089640845$ |
1.945996699 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 1323 a - 882\) , \( -63259 a + 173962\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1323a-882\right){x}-63259a+173962$ |
| 13475.3-b3 |
13475.3-b |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
13475.3 |
\( 5^{2} \cdot 7^{2} \cdot 11 \) |
\( 5^{6} \cdot 7^{4} \cdot 11^{18} \) |
$3.19313$ |
$(a-2), (-2a+1), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cn, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.089640845$ |
1.945996699 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -1321 a + 440\) , \( 64581 a + 110263\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1321a+440\right){x}+64581a+110263$ |
| 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 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 21593\) , \( 5467657\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+21593{x}+5467657$ |
| 43659.3-a3 |
43659.3-a |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
43659.3 |
\( 3^{4} \cdot 7^{2} \cdot 11 \) |
\( 3^{12} \cdot 7^{4} \cdot 11^{18} \) |
$4.28404$ |
$(-a), (a-1), (-2a+1), (7)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$6.706046397$ |
$0.066814341$ |
2.161523128 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 3966\) , \( 430965\bigr] \) |
${y}^2+{y}={x}^{3}+3966{x}+430965$ |
*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.
