| 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 |
| 24.2-a4 |
24.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
24.2 |
\( 2^{3} \cdot 3 \) |
\( 2^{11} \cdot 3^{4} \) |
$1.04658$ |
$(a+3), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.950378889$ |
1.474347858 |
\( -\frac{3992303075281}{81} a + \frac{10562789733245}{81} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -334 a - 894\) , \( -5836 a - 15456\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-334a-894\right){x}-5836a-15456$ |
| 24.2-b4 |
24.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
24.2 |
\( 2^{3} \cdot 3 \) |
\( 2^{11} \cdot 3^{4} \) |
$1.04658$ |
$(a+3), (-a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.371922271$ |
$18.72973460$ |
1.214009604 |
\( -\frac{3992303075281}{81} a + \frac{10562789733245}{81} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -336 a - 899\) , \( 5501 a + 14559\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-336a-899\right){x}+5501a+14559$ |
| 144.3-a4 |
144.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
144.3 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{11} \cdot 3^{10} \) |
$1.63798$ |
$(a+3), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.584693324$ |
0.976922250 |
\( -\frac{3992303075281}{81} a + \frac{10562789733245}{81} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 183 a - 626\) , \( 2690 a - 6743\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(183a-626\right){x}+2690a-6743$ |
| 144.3-c4 |
144.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
144.3 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{11} \cdot 3^{10} \) |
$1.63798$ |
$(a+3), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.711078438$ |
1.780620279 |
\( -\frac{3992303075281}{81} a + \frac{10562789733245}{81} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 184 a - 622\) , \( -2954 a + 6760\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(184a-622\right){x}-2954a+6760$ |
| 432.1-a4 |
432.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{11} \cdot 3^{10} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.255688621$ |
$4.711078438$ |
3.642274763 |
\( -\frac{3992303075281}{81} a + \frac{10562789733245}{81} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 10849 a - 28703\) , \( -998048 a + 2640583\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(10849a-28703\right){x}-998048a+2640583$ |
| 432.1-k4 |
432.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{11} \cdot 3^{10} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.584693324$ |
1.953844500 |
\( -\frac{3992303075281}{81} a + \frac{10562789733245}{81} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 10847 a - 28708\) , \( 1008896 a - 2669289\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(10847a-28708\right){x}+1008896a-2669289$ |
| 648.1-a4 |
648.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
648.1 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{11} \cdot 3^{16} \) |
$2.38568$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.243244867$ |
2.359724756 |
\( -\frac{3992303075281}{81} a + \frac{10562789733245}{81} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -3009 a - 8055\) , \( 140482 a + 372063\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3009a-8055\right){x}+140482a+372063$ |
| 648.1-p4 |
648.1-p |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
648.1 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{11} \cdot 3^{16} \) |
$2.38568$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.650126296$ |
0.982898572 |
\( -\frac{3992303075281}{81} a + \frac{10562789733245}{81} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -3010 a - 8059\) , \( -154565 a - 409263\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3010a-8059\right){x}-154565a-409263$ |
*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.
