| 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 |
| 96.6-a3 |
96.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
96.6 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3^{3} \) |
$1.60681$ |
$(-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$17.19445537$ |
2.244877865 |
\( \frac{383119}{9} a + \frac{909601}{9} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+{x}$ |
| 96.6-b3 |
96.6-b |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
96.6 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3^{3} \) |
$1.60681$ |
$(-a+3), (-2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.572684926$ |
$13.09983749$ |
1.958916616 |
\( \frac{383119}{9} a + \frac{909601}{9} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -103 a + 348\) , \( -4405 a + 14855\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-103a+348\right){x}-4405a+14855$ |
| 192.6-c3 |
192.6-c |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
192.6 |
\( 2^{6} \cdot 3 \) |
\( - 2^{15} \cdot 3^{3} \) |
$1.91082$ |
$(-a+3), (-2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.832232796$ |
$6.158529423$ |
3.036330193 |
\( \frac{383119}{9} a + \frac{909601}{9} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -516 a - 1224\) , \( -11451 a - 27165\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-516a-1224\right){x}-11451a-27165$ |
| 192.6-d3 |
192.6-d |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
192.6 |
\( 2^{6} \cdot 3 \) |
\( - 2^{15} \cdot 3^{3} \) |
$1.91082$ |
$(-a+3), (-2a+7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.063230808$ |
$18.28720428$ |
1.692341105 |
\( \frac{383119}{9} a + \frac{909601}{9} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 2 a + 14\) , \( -3 a + 27\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(2a+14\right){x}-3a+27$ |
| 288.6-e3 |
288.6-e |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
288.6 |
\( 2^{5} \cdot 3^{2} \) |
\( - 2^{9} \cdot 3^{9} \) |
$2.11468$ |
$(-a+3), (-2a+7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$9.927223440$ |
0.864053893 |
\( \frac{383119}{9} a + \frac{909601}{9} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -245 a - 581\) , \( 3455 a + 8196\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-245a-581\right){x}+3455a+8196$ |
| 288.6-f3 |
288.6-f |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
288.6 |
\( 2^{5} \cdot 3^{2} \) |
\( - 2^{9} \cdot 3^{9} \) |
$2.11468$ |
$(-a+3), (-2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.753402944$ |
$7.563194706$ |
3.967670656 |
\( \frac{383119}{9} a + \frac{909601}{9} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -7 a + 23\) , \( -76 a + 256\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7a+23\right){x}-76a+256$ |
| 576.7-i3 |
576.7-i |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.7 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{15} \cdot 3^{9} \) |
$2.51479$ |
$(-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.555628620$ |
1.237910991 |
\( \frac{383119}{9} a + \frac{909601}{9} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -190 a + 659\) , \( 11194 a - 37726\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-190a+659\right){x}+11194a-37726$ |
| 576.7-l3 |
576.7-l |
$4$ |
$4$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
576.7 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{15} \cdot 3^{9} \) |
$2.51479$ |
$(-a+3), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.55812231$ |
1.837933184 |
\( \frac{383119}{9} a + \frac{909601}{9} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -29 a - 68\) , \( 82 a + 195\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-29a-68\right){x}+82a+195$ |
*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.
