| 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 |
| 5547.2-a1 |
5547.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5547.2 |
\( 3 \cdot 43^{2} \) |
\( 3^{8} \cdot 43^{2} \) |
$1.33571$ |
$(-2a+1), (-7a+1), (7a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.099959152$ |
$2.545244737$ |
1.175117987 |
\( -\frac{799178752}{3483} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -19\) , \( 39\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-19{x}+39$ |
| 5547.2-b1 |
5547.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5547.2 |
\( 3 \cdot 43^{2} \) |
\( 3^{6} \cdot 43^{8} \) |
$1.33571$ |
$(-2a+1), (-7a+1), (7a-6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.648136583$ |
1.122605492 |
\( \frac{129784785047}{92307627} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 105\) , \( -191\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+105{x}-191$ |
| 5547.2-b2 |
5547.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5547.2 |
\( 3 \cdot 43^{2} \) |
\( 3^{12} \cdot 43^{4} \) |
$1.33571$ |
$(-2a+1), (-7a+1), (7a-6)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.296273166$ |
1.122605492 |
\( \frac{2845178713}{1347921} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -30\) , \( -29\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-30{x}-29$ |
| 5547.2-b3 |
5547.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5547.2 |
\( 3 \cdot 43^{2} \) |
\( 3^{3} \cdot 43^{10} \) |
$1.33571$ |
$(-2a+1), (-7a+1), (7a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.324068291$ |
1.122605492 |
\( -\frac{31773769007519668822}{105193802498409} a + \frac{18232756801575894611}{105193802498409} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -330 a + 1350\) , \( -17748 a + 3229\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-330a+1350\right){x}-17748a+3229$ |
| 5547.2-b4 |
5547.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5547.2 |
\( 3 \cdot 43^{2} \) |
\( 3^{3} \cdot 43^{10} \) |
$1.33571$ |
$(-2a+1), (-7a+1), (7a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.324068291$ |
1.122605492 |
\( \frac{31773769007519668822}{105193802498409} a - \frac{13541012205943774211}{105193802498409} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 330 a + 1020\) , \( 17748 a - 14519\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(330a+1020\right){x}+17748a-14519$ |
| 5547.2-b5 |
5547.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5547.2 |
\( 3 \cdot 43^{2} \) |
\( 3^{24} \cdot 43^{2} \) |
$1.33571$ |
$(-2a+1), (-7a+1), (7a-6)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.648136583$ |
1.122605492 |
\( \frac{1616855892553}{22851963} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -245\) , \( 1433\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-245{x}+1433$ |
| 5547.2-b6 |
5547.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5547.2 |
\( 3 \cdot 43^{2} \) |
\( 3^{6} \cdot 43^{2} \) |
$1.33571$ |
$(-2a+1), (-7a+1), (7a-6)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.592546333$ |
1.122605492 |
\( \frac{1630532233}{1161} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -25\) , \( -49\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-25{x}-49$ |
*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.
