| 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 |
| 13122.1-a1 |
13122.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13122.1 |
\( 2 \cdot 3^{8} \) |
\( 2^{4} \cdot 3^{12} \) |
$1.91280$ |
$(a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.305934883$ |
$3.305583379$ |
1.348391023 |
\( -\frac{35937}{4} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( -6\) , \( -8\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}-6{x}-8$ |
| 13122.1-a2 |
13122.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13122.1 |
\( 2 \cdot 3^{8} \) |
\( 2^{12} \cdot 3^{20} \) |
$1.91280$ |
$(a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cn, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.101978294$ |
$1.101861126$ |
1.348391023 |
\( \frac{109503}{64} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( 39\) , \( 19\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}+39{x}+19$ |
| 13122.1-b1 |
13122.1-b |
$4$ |
$21$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13122.1 |
\( 2 \cdot 3^{8} \) |
\( 2^{14} \cdot 3^{12} \) |
$1.91280$ |
$(a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.1, 7B |
$1$ |
\( 2 \cdot 3 \) |
$3.080173468$ |
$0.583485219$ |
2.396314257 |
\( -\frac{189613868625}{128} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( -1077\) , \( -13877\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}-1077{x}-13877$ |
| 13122.1-b2 |
13122.1-b |
$4$ |
$21$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13122.1 |
\( 2 \cdot 3^{8} \) |
\( 2^{6} \cdot 3^{20} \) |
$1.91280$ |
$(a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.2, 7B |
$1$ |
\( 2 \cdot 3 \) |
$0.146674927$ |
$1.361465512$ |
2.396314257 |
\( -\frac{140625}{8} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -42\) , \( -100\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-42{x}-100$ |
| 13122.1-b3 |
13122.1-b |
$4$ |
$21$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13122.1 |
\( 2 \cdot 3^{8} \) |
\( 2^{42} \cdot 3^{20} \) |
$1.91280$ |
$(a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.2, 7B |
$1$ |
\( 2 \cdot 3 \) |
$1.026724489$ |
$0.194495073$ |
2.396314257 |
\( -\frac{1159088625}{2097152} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( -852\) , \( -19664\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}-852{x}-19664$ |
| 13122.1-b4 |
13122.1-b |
$4$ |
$21$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13122.1 |
\( 2 \cdot 3^{8} \) |
\( 2^{2} \cdot 3^{12} \) |
$1.91280$ |
$(a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.1, 7B |
$1$ |
\( 2 \cdot 3 \) |
$0.440024781$ |
$4.084396538$ |
2.396314257 |
\( \frac{3375}{2} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 3\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+3{x}-1$ |
| 13122.1-c1 |
13122.1-c |
$4$ |
$21$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13122.1 |
\( 2 \cdot 3^{8} \) |
\( 2^{14} \cdot 3^{24} \) |
$1.91280$ |
$(a+1), (3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.2, 7B.2.3 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$0.194495073$ |
2.722931025 |
\( -\frac{189613868625}{128} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -9695\) , \( -364985\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-9695{x}-364985$ |
| 13122.1-c2 |
13122.1-c |
$4$ |
$21$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13122.1 |
\( 2 \cdot 3^{8} \) |
\( 2^{6} \cdot 3^{8} \) |
$1.91280$ |
$(a+1), (3)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.1, 7B.2.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$4.084396538$ |
2.722931025 |
\( -\frac{140625}{8} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -4\) , \( -5\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-4{x}-5$ |
| 13122.1-c3 |
13122.1-c |
$4$ |
$21$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13122.1 |
\( 2 \cdot 3^{8} \) |
\( 2^{42} \cdot 3^{8} \) |
$1.91280$ |
$(a+1), (3)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.1, 7B.2.3 |
$1$ |
\( 2 \cdot 3 \cdot 7 \) |
$1$ |
$0.583485219$ |
2.722931025 |
\( -\frac{1159088625}{2097152} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -95\) , \( -697\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-95{x}-697$ |
| 13122.1-c4 |
13122.1-c |
$4$ |
$21$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13122.1 |
\( 2 \cdot 3^{8} \) |
\( 2^{2} \cdot 3^{24} \) |
$1.91280$ |
$(a+1), (3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3, 7$ |
3B.1.2, 7B.2.1 |
$1$ |
\( 2 \) |
$1$ |
$1.361465512$ |
2.722931025 |
\( \frac{3375}{2} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( 26\) , \( -1\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+26{x}-1$ |
| 13122.1-d1 |
13122.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13122.1 |
\( 2 \cdot 3^{8} \) |
\( 2^{4} \cdot 3^{24} \) |
$1.91280$ |
$(a+1), (3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cn, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.101861126$ |
4.407444505 |
\( -\frac{35937}{4} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -56\) , \( -161\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-56{x}-161$ |
| 13122.1-d2 |
13122.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13122.1 |
\( 2 \cdot 3^{8} \) |
\( 2^{12} \cdot 3^{8} \) |
$1.91280$ |
$(a+1), (3)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$3.305583379$ |
4.407444505 |
\( \frac{109503}{64} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 4\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+4{x}-1$ |
*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.
