| 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 |
| 8.4-a1 |
8.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{377}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{22} \) |
$2.91798$ |
$(2,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$5.265518100$ |
$18.84084985$ |
5.109411999 |
\( -625 a + 6375 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 40 a - 408\) , \( -384 a + 3920\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(40a-408\right){x}-384a+3920$ |
| 8.4-a2 |
8.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{377}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{16} \) |
$2.91798$ |
$(2,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$5.265518100$ |
$18.84084985$ |
5.109411999 |
\( -1136625 a + 11604875 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 1092766 a - 11155180\) , \( 1940333321 a - 19807395878\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(1092766a-11155180\right){x}+1940333321a-19807395878$ |
| 8.4-a3 |
8.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{377}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{8} \) |
$2.91798$ |
$(2,a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$10.53103620$ |
$18.84084985$ |
5.109411999 |
\( 4875 a + 50375 \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 20 a + 104\) , \( 125 a - 235\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(20a+104\right){x}+125a-235$ |
| 8.4-a4 |
8.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{377}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{10} \) |
$2.91798$ |
$(2,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$21.06207240$ |
$4.710212463$ |
5.109411999 |
\( 508805125 a + 4685202125 \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -5 a + 359\) , \( 158 a - 574\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-5a+359\right){x}+158a-574$ |
| 8.4-b1 |
8.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{377}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{22} \) |
$2.91798$ |
$(2,a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$18.84084985$ |
0.485176567 |
\( -625 a + 6375 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -40 a - 368\) , \( -7856 a - 72340\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-40a-368\right){x}-7856a-72340$ |
| 8.4-b2 |
8.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{377}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{16} \) |
$2.91798$ |
$(2,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.84084985$ |
0.485176567 |
\( -1136625 a + 11604875 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a - 20\) , \( 9 a - 42\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-20\right){x}+9a-42$ |
| 8.4-b3 |
8.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{377}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{8} \) |
$2.91798$ |
$(2,a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$18.84084985$ |
0.485176567 |
\( 4875 a + 50375 \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -142 a - 1213\) , \( -4778 a - 43820\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-142a-1213\right){x}-4778a-43820$ |
| 8.4-b4 |
8.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{377}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{10} \) |
$2.91798$ |
$(2,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$4.710212463$ |
0.485176567 |
\( 508805125 a + 4685202125 \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -2447 a - 22438\) , \( -232511 a - 2140841\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-2447a-22438\right){x}-232511a-2140841$ |
*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.
