| 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 |
| 13122.5-a1 |
13122.5-a |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2^{3} \cdot 3^{22} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$1.514693616$ |
1.071050127 |
\( -\frac{1737}{4} a + 2421 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -14 a + 12\) , \( 22\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-14a+12\right){x}+22$ |
| 13122.5-a2 |
13122.5-a |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2 \cdot 3^{10} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$4.544080848$ |
1.071050127 |
\( -\frac{25263}{2} a + 2682 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( a - 3\) , \( -2 a + 3\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(a-3\right){x}-2a+3$ |
| 13122.5-b1 |
13122.5-b |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2^{4} \cdot 3^{12} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.305934883$ |
$3.305583379$ |
2.860369308 |
\( -\frac{35937}{4} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -6\) , \( 8\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-6{x}+8$ |
| 13122.5-b2 |
13122.5-b |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2^{12} \cdot 3^{20} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.101978294$ |
$1.101861126$ |
2.860369308 |
\( \frac{109503}{64} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 39\) , \( -19\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+39{x}-19$ |
| 13122.5-c1 |
13122.5-c |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2^{3} \cdot 3^{22} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$1.514693616$ |
1.071050127 |
\( \frac{1737}{4} a + 2421 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 13 a + 12\) , \( 22\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(13a+12\right){x}+22$ |
| 13122.5-c2 |
13122.5-c |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2 \cdot 3^{10} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$4.544080848$ |
1.071050127 |
\( \frac{25263}{2} a + 2682 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -2 a - 3\) , \( 2 a + 3\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-2a-3\right){x}+2a+3$ |
| 13122.5-d1 |
13122.5-d |
$4$ |
$21$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2^{14} \cdot 3^{12} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3, 7$ |
2Cn, 3B.1.1, 7B |
$1$ |
\( 2 \cdot 3^{2} \) |
$2.101119730$ |
$0.583485219$ |
3.467573330 |
\( -\frac{189613868625}{128} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -1077\) , \( 13877\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-1077{x}+13877$ |
| 13122.5-d2 |
13122.5-d |
$4$ |
$21$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2^{6} \cdot 3^{20} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3, 7$ |
2Cn, 3B.1.2, 7B |
$1$ |
\( 2 \) |
$0.900479884$ |
$1.361465512$ |
3.467573330 |
\( -\frac{140625}{8} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -42\) , \( -100\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-42{x}-100$ |
| 13122.5-d3 |
13122.5-d |
$4$ |
$21$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2^{42} \cdot 3^{20} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3, 7$ |
2Cn, 3B.1.2, 7B |
$1$ |
\( 2 \) |
$6.303359192$ |
$0.194495073$ |
3.467573330 |
\( -\frac{1159088625}{2097152} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -852\) , \( 19664\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-852{x}+19664$ |
| 13122.5-d4 |
13122.5-d |
$4$ |
$21$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2^{2} \cdot 3^{12} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3, 7$ |
2Cn, 3B.1.1, 7B |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.300159961$ |
$4.084396538$ |
3.467573330 |
\( \frac{3375}{2} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 3\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+3{x}-1$ |
| 13122.5-e1 |
13122.5-e |
$4$ |
$21$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2^{14} \cdot 3^{24} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3, 7$ |
2Cn, 3B.1.2, 7B.2.3 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$0.194495073$ |
1.925402993 |
\( -\frac{189613868625}{128} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -9695\) , \( -364985\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-9695{x}-364985$ |
| 13122.5-e2 |
13122.5-e |
$4$ |
$21$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2^{6} \cdot 3^{8} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3, 7$ |
2Cn, 3B.1.1, 7B.2.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$4.084396538$ |
1.925402993 |
\( -\frac{140625}{8} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -5\) , \( 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-5{x}+5$ |
| 13122.5-e3 |
13122.5-e |
$4$ |
$21$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2^{42} \cdot 3^{8} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3, 7$ |
2Cn, 3B.1.1, 7B.2.3 |
$1$ |
\( 2 \cdot 3 \cdot 7 \) |
$1$ |
$0.583485219$ |
1.925402993 |
\( -\frac{1159088625}{2097152} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -95\) , \( -697\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-95{x}-697$ |
| 13122.5-e4 |
13122.5-e |
$4$ |
$21$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2^{2} \cdot 3^{24} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3, 7$ |
2Cn, 3B.1.2, 7B.2.1 |
$1$ |
\( 2 \) |
$1$ |
$1.361465512$ |
1.925402993 |
\( \frac{3375}{2} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 25\) , \( 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+25{x}+1$ |
| 13122.5-f1 |
13122.5-f |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2^{3} \cdot 3^{10} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$4.544080848$ |
3.213150382 |
\( \frac{1737}{4} a + 2421 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( a + 1\) , \( -a - 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(a+1\right){x}-a-1$ |
| 13122.5-f2 |
13122.5-f |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2 \cdot 3^{22} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$1.514693616$ |
3.213150382 |
\( \frac{25263}{2} a + 2682 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -14 a - 29\) , \( -41 a - 39\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-14a-29\right){x}-41a-39$ |
| 13122.5-g1 |
13122.5-g |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2^{4} \cdot 3^{24} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$1.101861126$ |
3.116533897 |
\( -\frac{35937}{4} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -56\) , \( -161\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-56{x}-161$ |
| 13122.5-g2 |
13122.5-g |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2^{12} \cdot 3^{8} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$3.305583379$ |
3.116533897 |
\( \frac{109503}{64} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 4\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+4{x}-1$ |
| 13122.5-h1 |
13122.5-h |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2^{3} \cdot 3^{10} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$4.544080848$ |
3.213150382 |
\( -\frac{1737}{4} a + 2421 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -2 a + 1\) , \( -1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2a+1\right){x}-1$ |
| 13122.5-h2 |
13122.5-h |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
13122.5 |
\( 2 \cdot 3^{8} \) |
\( 2 \cdot 3^{22} \) |
$2.70510$ |
$(a), (-a-1), (a-1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$1.514693616$ |
3.213150382 |
\( -\frac{25263}{2} a + 2682 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 13 a - 29\) , \( 40 a - 39\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(13a-29\right){x}+40a-39$ |
*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.
