| 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 |
| 130.4-a1 |
130.4-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
130.4 |
\( 2 \cdot 5 \cdot 13 \) |
\( 2^{18} \cdot 5^{9} \cdot 13 \) |
$0.60347$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.960726389$ |
0.480363194 |
\( -\frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \) |
\( \bigl[i\) , \( i + 1\) , \( i\) , \( -89 i - 50\) , \( 368 i + 14\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-89i-50\right){x}+368i+14$ |
| 5200.6-b1 |
5200.6-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5200.6 |
\( 2^{4} \cdot 5^{2} \cdot 13 \) |
\( 2^{30} \cdot 5^{15} \cdot 13 \) |
$1.51764$ |
$(a+1), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1.318760694$ |
$0.214824951$ |
2.266421617 |
\( -\frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -269 i - 2036\) , \( 7244 i + 36407\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-269i-2036\right){x}+7244i+36407$ |
| 8450.9-a1 |
8450.9-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8450.9 |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{18} \cdot 5^{15} \cdot 13^{7} \) |
$1.71349$ |
$(a+1), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$2.048802786$ |
$0.119163442$ |
1.953139148 |
\( -\frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \) |
\( \bigl[i\) , \( i\) , \( 0\) , \( 6444 i + 1740\) , \( -79392 i - 200320\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+i{x}^{2}+\left(6444i+1740\right){x}-79392i-200320$ |
| 10530.4-a1 |
10530.4-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
10530.4 |
\( 2 \cdot 3^{4} \cdot 5 \cdot 13 \) |
\( 2^{18} \cdot 3^{12} \cdot 5^{9} \cdot 13 \) |
$1.81040$ |
$(a+1), (2a+1), (2a+3), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{4} \) |
$1$ |
$0.320242129$ |
2.882179168 |
\( -\frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \) |
\( \bigl[i\) , \( 1\) , \( 1\) , \( -806 i - 453\) , \( -11194 i - 21\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-806i-453\right){x}-11194i-21$ |
| 13520.6-c1 |
13520.6-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{30} \cdot 5^{9} \cdot 13^{7} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.133228779$ |
2.398118025 |
\( -\frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( 4206 i - 3289\) , \( 149030 i - 31276\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(4206i-3289\right){x}+149030i-31276$ |
| 16250.6-l1 |
16250.6-l |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.6 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{18} \cdot 5^{21} \cdot 13 \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.192145277$ |
3.458615002 |
\( -\frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \) |
\( \bigl[1\) , \( i - 1\) , \( 0\) , \( -2238 i - 1259\) , \( -50752 i + 1489\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-2238i-1259\right){x}-50752i+1489$ |
| 16640.4-g1 |
16640.4-g |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16640.4 |
\( 2^{8} \cdot 5 \cdot 13 \) |
\( 2^{42} \cdot 5^{9} \cdot 13 \) |
$2.02982$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.240181597$ |
2.161634376 |
\( -\frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1432 i + 806\) , \( -258 i + 25788\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(1432i+806\right){x}-258i+25788$ |
| 26000.4-g1 |
26000.4-g |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{30} \cdot 5^{15} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.473430659$ |
$0.214824951$ |
3.661369868 |
\( -\frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -1880 i + 828\) , \( 5448 i - 35920\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-1880i+828\right){x}+5448i-35920$ |
| 37570.10-c1 |
37570.10-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.10 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{18} \cdot 5^{9} \cdot 13 \cdot 17^{6} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{4} \) |
$0.079352997$ |
$0.233010375$ |
5.990783243 |
\( -\frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \) |
\( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( 1744 i + 39\) , \( 20027 i + 21608\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(1744i+39\right){x}+20027i+21608$ |
| 37570.12-b1 |
37570.12-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.12 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{18} \cdot 5^{9} \cdot 13 \cdot 17^{6} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.233010375$ |
2.097093378 |
\( -\frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \) |
\( \bigl[1\) , \( -i\) , \( i\) , \( 939 i + 1471\) , \( 18545 i - 20896\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(939i+1471\right){x}+18545i-20896$ |
| 42250.6-f1 |
42250.6-f |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.6 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{18} \cdot 5^{15} \cdot 13^{7} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.119163442$ |
2.144941969 |
\( -\frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \) |
\( \bigl[i\) , \( -i\) , \( 1\) , \( -134 i - 6674\) , \( -2410 i - 212803\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(-134i-6674\right){x}-2410i-212803$ |
| 66560.4-k1 |
66560.4-k |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
66560.4 |
\( 2^{10} \cdot 5 \cdot 13 \) |
\( 2^{48} \cdot 5^{9} \cdot 13 \) |
$2.87059$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{2} \) |
$1$ |
$0.169834036$ |
1.528506326 |
\( -\frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 1612 i - 2864\) , \( 52092 i - 51060\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(1612i-2864\right){x}+52092i-51060$ |
| 66560.4-p1 |
66560.4-p |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
66560.4 |
\( 2^{10} \cdot 5 \cdot 13 \) |
\( 2^{48} \cdot 5^{9} \cdot 13 \) |
$2.87059$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.169834036$ |
1.528506326 |
\( -\frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -1612 i + 2864\) , \( -51060 i - 52092\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-1612i+2864\right){x}-51060i-52092$ |
| 83200.6-i1 |
83200.6-i |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.6 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{42} \cdot 5^{15} \cdot 13 \) |
$3.03528$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{3} \) |
$1$ |
$0.107412475$ |
1.933424563 |
\( -\frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -1074 i - 8145\) , \( -56883 i - 283111\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-1074i-8145\right){x}-56883i-283111$ |
*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.
