| 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-a5 |
130.4-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
130.4 |
\( 2 \cdot 5 \cdot 13 \) |
\( 2^{2} \cdot 5 \cdot 13 \) |
$0.60347$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$8.646537506$ |
0.480363194 |
\( \frac{31409}{130} a + \frac{101344}{65} \) |
\( \bigl[i\) , \( i + 1\) , \( i\) , \( i\) , \( 0\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(i+1\right){x}^{2}+i{x}$ |
| 5200.6-b5 |
5200.6-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5200.6 |
\( 2^{4} \cdot 5^{2} \cdot 13 \) |
\( 2^{14} \cdot 5^{7} \cdot 13 \) |
$1.51764$ |
$(a+1), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.146528966$ |
$1.933424563$ |
2.266421617 |
\( \frac{31409}{130} a + \frac{101344}{65} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( 11 i + 4\) , \( -12 i - 1\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(11i+4\right){x}-12i-1$ |
| 8450.9-a5 |
8450.9-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8450.9 |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 5^{7} \cdot 13^{7} \) |
$1.71349$ |
$(a+1), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.227644754$ |
$1.072470984$ |
1.953139148 |
\( \frac{31409}{130} a + \frac{101344}{65} \) |
\( \bigl[i\) , \( i\) , \( 0\) , \( -26 i + 30\) , \( 54 i + 8\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+i{x}^{2}+\left(-26i+30\right){x}+54i+8$ |
| 10530.4-a5 |
10530.4-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
10530.4 |
\( 2 \cdot 3^{4} \cdot 5 \cdot 13 \) |
\( 2^{2} \cdot 3^{12} \cdot 5 \cdot 13 \) |
$1.81040$ |
$(a+1), (2a+1), (2a+3), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.882179168$ |
2.882179168 |
\( \frac{31409}{130} a + \frac{101344}{65} \) |
\( \bigl[i\) , \( 1\) , \( 1\) , \( 4 i - 3\) , \( 2 i - 3\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}+{x}^{2}+\left(4i-3\right){x}+2i-3$ |
| 13520.6-c5 |
13520.6-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{14} \cdot 5 \cdot 13^{7} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.199059012$ |
2.398118025 |
\( \frac{31409}{130} a + \frac{101344}{65} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( 6 i + 31\) , \( -2 i + 28\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(6i+31\right){x}-2i+28$ |
| 16250.6-l5 |
16250.6-l |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.6 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{2} \cdot 5^{13} \cdot 13 \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.729307501$ |
3.458615002 |
\( \frac{31409}{130} a + \frac{101344}{65} \) |
\( \bigl[1\) , \( i - 1\) , \( 0\) , \( 12 i - 9\) , \( -2 i - 11\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(12i-9\right){x}-2i-11$ |
| 16640.4-g5 |
16640.4-g |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16640.4 |
\( 2^{8} \cdot 5 \cdot 13 \) |
\( 2^{26} \cdot 5 \cdot 13 \) |
$2.02982$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.161634376$ |
2.161634376 |
\( \frac{31409}{130} a + \frac{101344}{65} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -8 i + 6\) , \( -2 i - 4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-8i+6\right){x}-2i-4$ |
| 26000.4-g5 |
26000.4-g |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{14} \cdot 5^{7} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.473430659$ |
$1.933424563$ |
3.661369868 |
\( \frac{31409}{130} a + \frac{101344}{65} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -12\) , \( 8 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}-12{x}+8i$ |
| 37570.10-c5 |
37570.10-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.10 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{2} \cdot 5 \cdot 13 \cdot 17^{6} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.714176977$ |
$2.097093378$ |
5.990783243 |
\( \frac{31409}{130} a + \frac{101344}{65} \) |
\( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( -6 i + 9\) , \( -11 i + 4\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-6i+9\right){x}-11i+4$ |
| 37570.12-b5 |
37570.12-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.12 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{2} \cdot 5 \cdot 13 \cdot 17^{6} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.097093378$ |
2.097093378 |
\( \frac{31409}{130} a + \frac{101344}{65} \) |
\( \bigl[1\) , \( -i\) , \( i\) , \( -11 i + 1\) , \( i + 2\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(-11i+1\right){x}+i+2$ |
| 42250.6-f5 |
42250.6-f |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.6 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{2} \cdot 5^{7} \cdot 13^{7} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.072470984$ |
2.144941969 |
\( \frac{31409}{130} a + \frac{101344}{65} \) |
\( \bigl[i\) , \( -i\) , \( 1\) , \( 36 i + 16\) , \( 30 i + 27\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(36i+16\right){x}+30i+27$ |
| 66560.4-k5 |
66560.4-k |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
66560.4 |
\( 2^{10} \cdot 5 \cdot 13 \) |
\( 2^{32} \cdot 5 \cdot 13 \) |
$2.87059$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.528506326$ |
1.528506326 |
\( \frac{31409}{130} a + \frac{101344}{65} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 12 i + 16\) , \( -4 i + 12\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(12i+16\right){x}-4i+12$ |
| 66560.4-p5 |
66560.4-p |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
66560.4 |
\( 2^{10} \cdot 5 \cdot 13 \) |
\( 2^{32} \cdot 5 \cdot 13 \) |
$2.87059$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.528506326$ |
1.528506326 |
\( \frac{31409}{130} a + \frac{101344}{65} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -12 i - 16\) , \( 12 i + 4\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-12i-16\right){x}+12i+4$ |
| 83200.6-i5 |
83200.6-i |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.6 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{26} \cdot 5^{7} \cdot 13 \) |
$3.03528$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.966712281$ |
1.933424563 |
\( \frac{31409}{130} a + \frac{101344}{65} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 46 i + 15\) , \( 45 i - 7\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(46i+15\right){x}+45i-7$ |
*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.
