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 |
4.2-a2 |
4.2-a |
$2$ |
$2$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{4} \) |
$3.04813$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$184.3090226$ |
1.701902269 |
\( -809793037 a^{2} - 144300549 a + 5498539288 \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 1117 a^{2} + 1696 a - 3548\) , \( -21789 a^{2} - 33080 a + 69221\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(1117a^{2}+1696a-3548\right){x}-21789a^{2}-33080a+69221$ |
16.3-b2 |
16.3-b |
$2$ |
$2$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{4} \) |
$3.84041$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$215.2987824$ |
1.988060494 |
\( -809793037 a^{2} - 144300549 a + 5498539288 \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} - a - 6\) , \( a^{2} - 4\) , \( 483 a^{2} + 734 a - 1528\) , \( -6060 a^{2} - 9202 a + 19247\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(483a^{2}+734a-1528\right){x}-6060a^{2}-9202a+19247$ |
64.4-f2 |
64.4-f |
$2$ |
$2$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{10} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$50.04044596$ |
3.696572087 |
\( -809793037 a^{2} - 144300549 a + 5498539288 \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + 4\) , \( a^{2} + a - 4\) , \( -19 a^{2} + 65 a - 48\) , \( 90 a^{2} - 333 a + 268\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-19a^{2}+65a-48\right){x}+90a^{2}-333a+268$ |
64.4-i1 |
64.4-i |
$2$ |
$2$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{10} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.626129519$ |
$42.83770479$ |
3.859407168 |
\( -809793037 a^{2} - 144300549 a + 5498539288 \) |
\( \bigl[a^{2} - 4\) , \( -1\) , \( 0\) , \( -a^{2} + 5 a - 5\) , \( -2 a^{2} + 8 a - 7\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}={x}^{3}-{x}^{2}+\left(-a^{2}+5a-5\right){x}-2a^{2}+8a-7$ |
100.4-a1 |
100.4-a |
$2$ |
$2$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
100.4 |
\( 2^{2} \cdot 5^{2} \) |
\( - 2^{4} \cdot 5^{6} \) |
$5.21223$ |
$(a^2-6), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$27.30099104$ |
1.008385112 |
\( -809793037 a^{2} - 144300549 a + 5498539288 \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - 4\) , \( a^{2} - 4\) , \( -25 a^{2} + 98 a - 84\) , \( 75 a^{2} - 274 a + 217\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-25a^{2}+98a-84\right){x}+75a^{2}-274a+217$ |
196.4-d2 |
196.4-d |
$2$ |
$2$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
196.4 |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{4} \cdot 7^{6} \) |
$5.83087$ |
$(a^2-6), (a^2+2a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.062503022$ |
$81.37529086$ |
1.690768289 |
\( -809793037 a^{2} - 144300549 a + 5498539288 \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} - 6\) , \( a^{2} - 4\) , \( 78352 a^{2} + 118955 a - 248912\) , \( -13546907 a^{2} - 20566897 a + 43036813\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(78352a^{2}+118955a-248912\right){x}-13546907a^{2}-20566897a+43036813$ |
*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.