| 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 |
| 2.1-b1 |
2.1-b |
$4$ |
$6$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{18} \) |
$2.71558$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1.651286898$ |
$9.329326956$ |
0.853516891 |
\( -\frac{1308241604941929}{262144} a^{2} - \frac{233087636858447}{262144} a + \frac{8883119257726807}{262144} \) |
\( \bigl[a^{2} - 5\) , \( 0\) , \( a + 1\) , \( 18957864 a^{2} + 3380608 a - 128731016\) , \( 72417315372 a^{2} + 12904890246 a - 491718787736\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(18957864a^{2}+3380608a-128731016\right){x}+72417315372a^{2}+12904890246a-491718787736$ |
| 16.3-d3 |
16.3-d |
$4$ |
$6$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{30} \) |
$3.84041$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$9.196610761$ |
1.528580560 |
\( -\frac{1308241604941929}{262144} a^{2} - \frac{233087636858447}{262144} a + \frac{8883119257726807}{262144} \) |
\( \bigl[a\) , \( -a^{2} + a + 5\) , \( a\) , \( 5575750 a^{2} + 993573 a - 37859656\) , \( 11556551448 a^{2} + 2059308953 a - 78469594148\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(5575750a^{2}+993573a-37859656\right){x}+11556551448a^{2}+2059308953a-78469594148$ |
| 50.2-e1 |
50.2-e |
$4$ |
$6$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
50.2 |
\( 2 \cdot 5^{2} \) |
\( - 2^{18} \cdot 5^{6} \) |
$4.64357$ |
$(a^2-6), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.665824085$ |
$31.39097744$ |
2.315973615 |
\( -\frac{1308241604941929}{262144} a^{2} - \frac{233087636858447}{262144} a + \frac{8883119257726807}{262144} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} + a - 4\) , \( a + 1\) , \( 183 a^{2} + 45 a - 1267\) , \( -2063 a^{2} - 544 a + 14454\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(183a^{2}+45a-1267\right){x}-2063a^{2}-544a+14454$ |
| 64.4-c3 |
64.4-c |
$4$ |
$6$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{36} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1.123921439$ |
$26.84809856$ |
3.343634184 |
\( -\frac{1308241604941929}{262144} a^{2} - \frac{233087636858447}{262144} a + \frac{8883119257726807}{262144} \) |
\( \bigl[a^{2} + a - 4\) , \( a + 1\) , \( 0\) , \( 26312511 a^{2} + 4706405 a - 178707809\) , \( -118384210425 a^{2} - 21084547314 a + 803807796043\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(26312511a^{2}+4706405a-178707809\right){x}-118384210425a^{2}-21084547314a+803807796043$ |
| 64.4-l1 |
64.4-l |
$4$ |
$6$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{36} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$52.93233119$ |
0.977550130 |
\( -\frac{1308241604941929}{262144} a^{2} - \frac{233087636858447}{262144} a + \frac{8883119257726807}{262144} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} + a - 6\) , \( a^{2} + a - 4\) , \( 828801944 a^{2} + 147688893 a - 5627612208\) , \( -20926676404274 a^{2} - 3729010063602 a + 142093238039116\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(828801944a^{2}+147688893a-5627612208\right){x}-20926676404274a^{2}-3729010063602a+142093238039116$ |
| 98.2-e3 |
98.2-e |
$4$ |
$6$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( - 2^{18} \cdot 7^{6} \) |
$5.19471$ |
$(a^2-6), (a^2+2a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.859378336$ |
$6.951984279$ |
5.958061197 |
\( -\frac{1308241604941929}{262144} a^{2} - \frac{233087636858447}{262144} a + \frac{8883119257726807}{262144} \) |
\( \bigl[a + 1\) , \( -a^{2} - a + 4\) , \( a^{2} - 4\) , \( 203 a^{2} + 84 a - 1502\) , \( 3399 a^{2} - 972 a - 19108\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(203a^{2}+84a-1502\right){x}+3399a^{2}-972a-19108$ |
*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.
