| 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 |
| 21609.1-a1 |
21609.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
21609.1 |
\( 3^{2} \cdot 7^{4} \) |
\( 3^{2} \cdot 7^{28} \) |
$2.16684$ |
$(3), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.123153847$ |
1.970461553 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -1666\) , \( -72764\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-1666{x}-72764$ |
| 21609.1-a2 |
21609.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
21609.1 |
\( 3^{2} \cdot 7^{4} \) |
\( 3^{4} \cdot 7^{14} \) |
$2.16684$ |
$(3), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.985230776$ |
1.970461553 |
\( \frac{103823}{63} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( 49\) , \( -48\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}+49{x}-48$ |
| 21609.1-a3 |
21609.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
21609.1 |
\( 3^{2} \cdot 7^{4} \) |
\( 3^{8} \cdot 7^{16} \) |
$2.16684$ |
$(3), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$0.492615388$ |
1.970461553 |
\( \frac{7189057}{3969} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -196\) , \( -146\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-196{x}-146$ |
| 21609.1-a4 |
21609.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
21609.1 |
\( 3^{2} \cdot 7^{4} \) |
\( 3^{16} \cdot 7^{14} \) |
$2.16684$ |
$(3), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.246307694$ |
1.970461553 |
\( \frac{6570725617}{45927} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -1911\) , \( 32782\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-1911{x}+32782$ |
| 21609.1-a5 |
21609.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
21609.1 |
\( 3^{2} \cdot 7^{4} \) |
\( 3^{4} \cdot 7^{20} \) |
$2.16684$ |
$(3), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$16$ |
\( 2^{3} \) |
$1$ |
$0.246307694$ |
1.970461553 |
\( \frac{13027640977}{21609} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -2401\) , \( -44246\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-2401{x}-44246$ |
| 21609.1-a6 |
21609.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
21609.1 |
\( 3^{2} \cdot 7^{4} \) |
\( 3^{2} \cdot 7^{16} \) |
$2.16684$ |
$(3), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.123153847$ |
1.970461553 |
\( \frac{53297461115137}{147} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -38416\) , \( -2882228\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-38416{x}-2882228$ |
| 21609.1-b1 |
21609.1-b |
$2$ |
$13$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
21609.1 |
\( 3^{2} \cdot 7^{4} \) |
\( 3^{26} \cdot 7^{16} \) |
$2.16684$ |
$(3), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$13$ |
13B.3.2 |
$1$ |
\( 3 \cdot 13 \) |
$1$ |
$0.059565157$ |
2.323041160 |
\( -\frac{1713910976512}{1594323} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -44704\) , \( -3655907\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-44704{x}-3655907$ |
| 21609.1-b2 |
21609.1-b |
$2$ |
$13$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
21609.1 |
\( 3^{2} \cdot 7^{4} \) |
\( 3^{2} \cdot 7^{16} \) |
$2.16684$ |
$(3), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$13$ |
13B.3.1 |
$1$ |
\( 3 \) |
$1$ |
$0.774347053$ |
2.323041160 |
\( -\frac{28672}{3} \) |
\( \bigl[0\) , \( -1\) , \( i\) , \( -114\) , \( -473\bigr] \) |
${y}^2+i{y}={x}^{3}-{x}^{2}-114{x}-473$ |
| 21609.1-c1 |
21609.1-c |
$2$ |
$13$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
21609.1 |
\( 3^{2} \cdot 7^{4} \) |
\( 3^{26} \cdot 7^{4} \) |
$2.16684$ |
$(3), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$13$ |
13B.4.2 |
$1$ |
\( 13 \) |
$1$ |
$0.416956105$ |
5.420429375 |
\( -\frac{1713910976512}{1594323} \) |
\( \bigl[0\) , \( 1\) , \( i\) , \( -912\) , \( -10919\bigr] \) |
${y}^2+i{y}={x}^{3}+{x}^{2}-912{x}-10919$ |
| 21609.1-c2 |
21609.1-c |
$2$ |
$13$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
21609.1 |
\( 3^{2} \cdot 7^{4} \) |
\( 3^{2} \cdot 7^{4} \) |
$2.16684$ |
$(3), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$13$ |
13B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$5.420429375$ |
5.420429375 |
\( -\frac{28672}{3} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-2{x}-1$ |
*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.
