| 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 |
| 1444.2-a1 |
1444.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1444.2 |
\( 2^{2} \cdot 19^{2} \) |
\( 2^{2} \cdot 19^{10} \) |
$0.95409$ |
$(-5a+3), (-5a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.965055962$ |
1.114350639 |
\( -\frac{37966934881}{4952198} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -70\) , \( -279\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-70{x}-279$ |
| 1444.2-a2 |
1444.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1444.2 |
\( 2^{2} \cdot 19^{2} \) |
\( 2^{10} \cdot 19^{2} \) |
$0.95409$ |
$(-5a+3), (-5a+2), (2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$4.825279813$ |
1.114350639 |
\( -\frac{1}{608} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+1$ |
| 1444.2-b1 |
1444.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1444.2 |
\( 2^{2} \cdot 19^{2} \) |
\( 2^{6} \cdot 19^{10} \) |
$0.95409$ |
$(-5a+3), (-5a+2), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$0.378954466$ |
1.312736779 |
\( -\frac{76700843487905758375}{2581501582232} a + \frac{3659396196412919000}{322687697779} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 1809 a - 330\) , \( 7600 a + 21674\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(1809a-330\right){x}+7600a+21674$ |
| 1444.2-b2 |
1444.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1444.2 |
\( 2^{2} \cdot 19^{2} \) |
\( 2^{6} \cdot 19^{10} \) |
$0.95409$ |
$(-5a+3), (-5a+2), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$0.378954466$ |
1.312736779 |
\( \frac{76700843487905758375}{2581501582232} a - \frac{47425673916602406375}{2581501582232} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -1810 a + 1480\) , \( -7600 a + 29274\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-1810a+1480\right){x}-7600a+29274$ |
| 1444.2-b3 |
1444.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1444.2 |
\( 2^{2} \cdot 19^{2} \) |
\( 2^{6} \cdot 19^{2} \) |
$0.95409$ |
$(-5a+3), (-5a+2), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$3.410590199$ |
1.312736779 |
\( -\frac{413493625}{152} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 15 a\) , \( 22\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+15a{x}+22$ |
| 1444.2-b4 |
1444.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1444.2 |
\( 2^{2} \cdot 19^{2} \) |
\( 2^{54} \cdot 19^{2} \) |
$0.95409$ |
$(-5a+3), (-5a+2), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$0.378954466$ |
1.312736779 |
\( -\frac{69173457625}{2550136832} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 85 a\) , \( -2456\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+85a{x}-2456$ |
| 1444.2-b5 |
1444.2-b |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1444.2 |
\( 2^{2} \cdot 19^{2} \) |
\( 2^{18} \cdot 19^{6} \) |
$0.95409$ |
$(-5a+3), (-5a+2), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{4} \) |
$1$ |
$1.136863399$ |
1.312736779 |
\( \frac{94196375}{3511808} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -10 a\) , \( 90\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-10a{x}+90$ |
*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.
