| 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 |
| 650.4-a1 |
650.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
650.4 |
\( 2 \cdot 5^{2} \cdot 13 \) |
\( 2^{4} \cdot 5^{7} \cdot 13^{3} \) |
$0.90240$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.964283096$ |
1.446424644 |
\( \frac{1411302663595036}{34328125} a - \frac{1774751413484333}{137312500} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( 161 i - 221\) , \( -1400 i + 996\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(161i-221\right){x}-1400i+996$ |
| 650.4-a2 |
650.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
650.4 |
\( 2 \cdot 5^{2} \cdot 13 \) |
\( 2^{12} \cdot 5^{5} \cdot 13 \) |
$0.90240$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$2.892849288$ |
1.446424644 |
\( \frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( i - 1\) , \( -4 i + 4\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}-4i+4$ |
| 650.4-a3 |
650.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
650.4 |
\( 2 \cdot 5^{2} \cdot 13 \) |
\( 2 \cdot 5^{25} \cdot 13^{3} \) |
$0.90240$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$0.241070774$ |
1.446424644 |
\( -\frac{94290382838862669189021}{261902809143066406250} a + \frac{23228384730714798359947}{261902809143066406250} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( -474 i + 144\) , \( -8233 i + 3785\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-474i+144\right){x}-8233i+3785$ |
| 650.4-a4 |
650.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
650.4 |
\( 2 \cdot 5^{2} \cdot 13 \) |
\( 2^{3} \cdot 5^{14} \cdot 13^{4} \) |
$0.90240$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$0.723212322$ |
1.446424644 |
\( \frac{20122730162024161}{27891601562500} a + \frac{104798752060117927}{27891601562500} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( -109 i + 9\) , \( 170 i - 274\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-109i+9\right){x}+170i-274$ |
| 650.4-a5 |
650.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
650.4 |
\( 2 \cdot 5^{2} \cdot 13 \) |
\( 2^{2} \cdot 5^{14} \cdot 13^{6} \) |
$0.90240$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.482141548$ |
1.446424644 |
\( \frac{12415547946147007137}{2356840332031250} a + \frac{5474429230691529908}{1178420166015625} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( 171 i - 221\) , \( -1272 i + 1038\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(171i-221\right){x}-1272i+1038$ |
| 650.4-a6 |
650.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
650.4 |
\( 2 \cdot 5^{2} \cdot 13 \) |
\( 2 \cdot 5^{10} \cdot 13^{12} \) |
$0.90240$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.241070774$ |
1.446424644 |
\( -\frac{4240925829815707588031}{728065160077531250} a + \frac{3613304062782124177817}{728065160077531250} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( 976 i - 586\) , \( 13841 i + 979\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(976i-586\right){x}+13841i+979$ |
| 650.4-a7 |
650.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
650.4 |
\( 2 \cdot 5^{2} \cdot 13 \) |
\( 2^{6} \cdot 5^{10} \cdot 13^{2} \) |
$0.90240$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$1.446424644$ |
1.446424644 |
\( -\frac{117057737097}{21125000} a + \frac{49160487287}{2640625} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( -39 i - 1\) , \( -68 i + 60\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-39i-1\right){x}-68i+60$ |
| 650.4-a8 |
650.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
650.4 |
\( 2 \cdot 5^{2} \cdot 13 \) |
\( 2^{3} \cdot 5^{11} \cdot 13 \) |
$0.90240$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.723212322$ |
1.446424644 |
\( -\frac{4023422266102893}{20312500} a + \frac{5856979210600901}{20312500} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( -609 i - 11\) , \( -4242 i + 3978\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-609i-11\right){x}-4242i+3978$ |
*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.
