| 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 |
| 14641.1-a1 |
14641.1-a |
$2$ |
$11$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14641.1 |
\( 11^{4} \) |
\( 11^{18} \) |
$1.70252$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.8 |
$1$ |
\( 2 \) |
$0.987636717$ |
$0.316083258$ |
1.441876556 |
\( -32768 \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -887 a + 887\) , \( -10143\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-887a+887\right){x}-10143$ |
| 14641.1-a2 |
14641.1-a |
$2$ |
$11$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14641.1 |
\( 11^{4} \) |
\( 11^{6} \) |
$1.70252$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.3 |
$1$ |
\( 2 \) |
$0.089785156$ |
$3.476915842$ |
1.441876556 |
\( -32768 \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -7 a + 7\) , \( 10\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-7a+7\right){x}+10$ |
| 14641.1-b1 |
14641.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14641.1 |
\( 11^{4} \) |
\( 11^{14} \) |
$1.70252$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \) |
$7.655751664$ |
$0.033664429$ |
2.380775540 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -946260 a + 946260\) , \( 354609639\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-946260a+946260\right){x}+354609639$ |
| 14641.1-b2 |
14641.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14641.1 |
\( 11^{4} \) |
\( 11^{22} \) |
$1.70252$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2^{2} \) |
$1.531150332$ |
$0.168322147$ |
2.380775540 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -1250 a + 1250\) , \( 31239\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-1250a+1250\right){x}+31239$ |
| 14641.1-b3 |
14641.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14641.1 |
\( 11^{4} \) |
\( 11^{14} \) |
$1.70252$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.306230066$ |
$0.841610737$ |
2.380775540 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -40 a + 40\) , \( -221\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-40a+40\right){x}-221$ |
| 14641.1-c1 |
14641.1-c |
$2$ |
$11$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14641.1 |
\( 11^{4} \) |
\( 11^{16} \) |
$1.70252$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.5 |
$1$ |
\( 3 \) |
$1.460386125$ |
$0.256154731$ |
2.591735630 |
\( -24729001 \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 3632 a\) , \( 82757\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+3632a{x}+82757$ |
| 14641.1-c2 |
14641.1-c |
$2$ |
$11$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14641.1 |
\( 11^{4} \) |
\( 11^{8} \) |
$1.70252$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.7 |
$1$ |
\( 3 \) |
$0.132762375$ |
$2.817702048$ |
2.591735630 |
\( -121 \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 2 a\) , \( -7\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+2a{x}-7$ |
| 14641.1-d1 |
14641.1-d |
$2$ |
$11$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14641.1 |
\( 11^{4} \) |
\( 11^{4} \) |
$1.70252$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.6 |
$1$ |
\( 1 \) |
$0.467099783$ |
$2.817702048$ |
3.039513647 |
\( -24729001 \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 29 a\) , \( -76\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+29a{x}-76$ |
| 14641.1-d2 |
14641.1-d |
$2$ |
$11$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14641.1 |
\( 11^{4} \) |
\( 11^{20} \) |
$1.70252$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.4 |
$1$ |
\( 1 \) |
$5.138097620$ |
$0.256154731$ |
3.039513647 |
\( -121 \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 304 a\) , \( 7888\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+304a{x}+7888$ |
*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.
