| 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-c1 |
2.1-c |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{2} \) |
$2.71558$ |
$(a^2-6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$282.8497870$ |
1.305911907 |
\( \frac{38239925}{4} a^{2} + \frac{58077475}{4} a - \frac{121417863}{4} \) |
\( \bigl[a^{2} - 5\) , \( -a + 1\) , \( 1\) , \( -1022218105 a^{2} - 1551930198 a + 3247458136\) , \( 33252622286582 a^{2} + 50484087904678 a - 105639391507833\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1022218105a^{2}-1551930198a+3247458136\right){x}+33252622286582a^{2}+50484087904678a-105639391507833$ |
| 16.3-f5 |
16.3-f |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{14} \) |
$3.84041$ |
$(a^2-6)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$148.1392886$ |
0.341978091 |
\( \frac{38239925}{4} a^{2} + \frac{58077475}{4} a - \frac{121417863}{4} \) |
\( \bigl[a\) , \( -a^{2} + 4\) , \( 0\) , \( -57 a^{2} - 84 a + 181\) , \( 442 a^{2} + 670 a - 1402\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-57a^{2}-84a+181\right){x}+442a^{2}+670a-1402$ |
| 50.2-f5 |
50.2-f |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
50.2 |
\( 2 \cdot 5^{2} \) |
\( 2^{2} \cdot 5^{6} \) |
$4.64357$ |
$(a^2-6), (-a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$210.8740687$ |
3.894405722 |
\( \frac{38239925}{4} a^{2} + \frac{58077475}{4} a - \frac{121417863}{4} \) |
\( \bigl[a + 1\) , \( a^{2} - 6\) , \( a^{2} + a - 4\) , \( -179117827763 a^{2} - 271936453135 a + 569034771759\) , \( 77128139875864374 a^{2} + 117095841640997417 a - 245026383014167679\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-179117827763a^{2}-271936453135a+569034771759\right){x}+77128139875864374a^{2}+117095841640997417a-245026383014167679$ |
| 64.4-e3 |
64.4-e |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{20} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.493594424$ |
$55.50090546$ |
2.296370864 |
\( \frac{38239925}{4} a^{2} + \frac{58077475}{4} a - \frac{121417863}{4} \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} + a - 4\) , \( 0\) , \( -11371 a^{2} - 17263 a + 36124\) , \( -1275372 a^{2} - 1936268 a + 4051696\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-11371a^{2}-17263a+36124\right){x}-1275372a^{2}-1936268a+4051696$ |
| 64.4-j1 |
64.4-j |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{20} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$58.13590838$ |
0.536824692 |
\( \frac{38239925}{4} a^{2} + \frac{58077475}{4} a - \frac{121417863}{4} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} - a + 6\) , \( a^{2} - 4\) , \( -4937 a^{2} - 7494 a + 15688\) , \( -350350 a^{2} - 531900 a + 1113020\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(-4937a^{2}-7494a+15688\right){x}-350350a^{2}-531900a+1113020$ |
| 98.2-h3 |
98.2-h |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{6} \) |
$5.19471$ |
$(a^2-6), (a^2+2a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$111.9827763$ |
2.068089108 |
\( \frac{38239925}{4} a^{2} + \frac{58077475}{4} a - \frac{121417863}{4} \) |
\( \bigl[1\) , \( a^{2} - a - 6\) , \( a^{2} - 5\) , \( -71745632309 a^{2} - 108924125652 a + 227926834626\) , \( 19552397448061728 a^{2} + 29684424374358989 a - 62115503286670144\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-71745632309a^{2}-108924125652a+227926834626\right){x}+19552397448061728a^{2}+29684424374358989a-62115503286670144$ |
*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.
