| 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 |
| 14400.7-k1 |
14400.7-k |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.7 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{15} \cdot 5^{4} \) |
$3.24658$ |
$(a-1), (-a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$0.637697734$ |
3.076369620 |
\( \frac{10718164}{19683} a - \frac{2692192}{6561} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -56 a + 29\) , \( -88 a + 542\bigr] \) |
${y}^2={x}^{3}+\left(-56a+29\right){x}-88a+542$ |
| 14400.7-l1 |
14400.7-l |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
14400.7 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{15} \cdot 5^{10} \) |
$3.24658$ |
$(a-1), (-a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$9$ |
\( 2^{2} \) |
$1$ |
$0.285187096$ |
6.191074436 |
\( \frac{10718164}{19683} a - \frac{2692192}{6561} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 31 a + 446\) , \( 2784 a - 4906\bigr] \) |
${y}^2={x}^{3}+\left(31a+446\right){x}+2784a-4906$ |
| 19200.4-c1 |
19200.4-c |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
19200.4 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{9} \cdot 5^{10} \) |
$3.48867$ |
$(a-1), (-a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$0.493958540$ |
1.191472830 |
\( \frac{10718164}{19683} a - \frac{2692192}{6561} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 43 a - 160\) , \( 191 a - 1121\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(43a-160\right){x}+191a-1121$ |
| 19200.4-d1 |
19200.4-d |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
19200.4 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{9} \cdot 5^{4} \) |
$3.48867$ |
$(a-1), (-a-1), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$0.019114707$ |
$1.104524875$ |
5.499972963 |
\( \frac{10718164}{19683} a - \frac{2692192}{6561} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 16 a + 8\) , \( 32 a + 64\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(16a+8\right){x}+32a+64$ |
| 19200.4-bf1 |
19200.4-bf |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
19200.4 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{9} \cdot 5^{4} \) |
$3.48867$ |
$(a-1), (-a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.104524875$ |
3.996321364 |
\( \frac{10718164}{19683} a - \frac{2692192}{6561} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 16 a + 8\) , \( -32 a - 64\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(16a+8\right){x}-32a-64$ |
| 19200.4-bg1 |
19200.4-bg |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
19200.4 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{9} \cdot 5^{10} \) |
$3.48867$ |
$(a-1), (-a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.493958540$ |
5.361627738 |
\( \frac{10718164}{19683} a - \frac{2692192}{6561} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 43 a - 160\) , \( -191 a + 1121\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(43a-160\right){x}-191a+1121$ |
| 43200.4-d1 |
43200.4-d |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
43200.4 |
\( 2^{6} \cdot 3^{3} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{15} \cdot 5^{10} \) |
$4.27273$ |
$(-a), (a-1), (-a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.285187096$ |
0.343948579 |
\( \frac{10718164}{19683} a - \frac{2692192}{6561} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -244 a + 348\) , \( 1532 a + 4160\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-244a+348\right){x}+1532a+4160$ |
| 43200.4-w1 |
43200.4-w |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
43200.4 |
\( 2^{6} \cdot 3^{3} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{15} \cdot 5^{4} \) |
$4.27273$ |
$(-a), (a-1), (-a-1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3^{3} \) |
$0.211675847$ |
$0.637697734$ |
8.791107477 |
\( \frac{10718164}{19683} a - \frac{2692192}{6561} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -22 a - 75\) , \( -311 a - 74\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-22a-75\right){x}-311a-74$ |
*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.
