| 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-a3 |
539.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
539.1 |
\( 7^{2} \cdot 11 \) |
\( 7^{4} \cdot 11^{18} \) |
$2.47339$ |
$(-4a-9), (7)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.602881548$ |
1.679171307 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -162165 a + 546870\) , \( -270199791 a + 911189707\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-162165a+546870\right){x}-270199791a+911189707$ |
| 539.1-f3 |
539.1-f |
$3$ |
$9$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
539.1 |
\( 7^{2} \cdot 11 \) |
\( 7^{4} \cdot 11^{18} \) |
$2.47339$ |
$(-4a-9), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$6.706046397$ |
$0.266569154$ |
2.489484723 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+441{x}-15815$ |
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*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.
