| 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-a2 |
130.4-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
130.4 |
\( 2 \cdot 5 \cdot 13 \) |
\( 2^{6} \cdot 5^{3} \cdot 13^{3} \) |
$0.60347$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.882179168$ |
0.480363194 |
\( \frac{37525044319}{2197000} a - \frac{7169596274}{274625} \) |
\( \bigl[i\) , \( i + 1\) , \( i\) , \( -9 i + 5\) , \( -2 i + 18\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-9i+5\right){x}-2i+18$ |
| 5200.6-b2 |
5200.6-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5200.6 |
\( 2^{4} \cdot 5^{2} \cdot 13 \) |
\( 2^{18} \cdot 5^{9} \cdot 13^{3} \) |
$1.51764$ |
$(a+1), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \) |
$0.439586898$ |
$0.644474854$ |
2.266421617 |
\( \frac{37525044319}{2197000} a - \frac{7169596274}{274625} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -189 i - 96\) , \( -1128 i + 111\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-189i-96\right){x}-1128i+111$ |
| 8450.9-a2 |
8450.9-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8450.9 |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 5^{9} \cdot 13^{9} \) |
$1.71349$ |
$(a+1), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \) |
$0.682934262$ |
$0.357490328$ |
1.953139148 |
\( \frac{37525044319}{2197000} a - \frac{7169596274}{274625} \) |
\( \bigl[i\) , \( i\) , \( 0\) , \( 524 i - 445\) , \( 6620 i - 2129\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+i{x}^{2}+\left(524i-445\right){x}+6620i-2129$ |
| 10530.4-a2 |
10530.4-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
10530.4 |
\( 2 \cdot 3^{4} \cdot 5 \cdot 13 \) |
\( 2^{6} \cdot 3^{12} \cdot 5^{3} \cdot 13^{3} \) |
$1.81040$ |
$(a+1), (2a+1), (2a+3), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$0.960726389$ |
2.882179168 |
\( \frac{37525044319}{2197000} a - \frac{7169596274}{274625} \) |
\( \bigl[i\) , \( 1\) , \( 1\) , \( -86 i + 42\) , \( 11 i - 354\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-86i+42\right){x}+11i-354$ |
| 13520.6-c2 |
13520.6-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{18} \cdot 5^{3} \cdot 13^{9} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.399686337$ |
2.398118025 |
\( \frac{37525044319}{2197000} a - \frac{7169596274}{274625} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -34 i - 549\) , \( 438 i + 5056\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-34i-549\right){x}+438i+5056$ |
| 16250.6-l2 |
16250.6-l |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.6 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{6} \cdot 5^{15} \cdot 13^{3} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.576435833$ |
3.458615002 |
\( \frac{37525044319}{2197000} a - \frac{7169596274}{274625} \) |
\( \bigl[1\) , \( i - 1\) , \( 0\) , \( -238 i + 116\) , \( 248 i - 1636\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-238i+116\right){x}+248i-1636$ |
| 16640.4-g2 |
16640.4-g |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16640.4 |
\( 2^{8} \cdot 5 \cdot 13 \) |
\( 2^{30} \cdot 5^{3} \cdot 13^{3} \) |
$2.02982$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.720544792$ |
2.161634376 |
\( \frac{37525044319}{2197000} a - \frac{7169596274}{274625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 152 i - 74\) , \( -914 i - 52\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(152i-74\right){x}-914i-52$ |
| 26000.4-g2 |
26000.4-g |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{18} \cdot 5^{9} \cdot 13^{3} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.157810219$ |
$0.644474854$ |
3.661369868 |
\( \frac{37525044319}{2197000} a - \frac{7169596274}{274625} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -40 i + 208\) , \( 1120 i + 384\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-40i+208\right){x}+1120i+384$ |
| 37570.10-c2 |
37570.10-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.10 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{6} \cdot 5^{3} \cdot 13^{3} \cdot 17^{6} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.238058992$ |
$0.699031126$ |
5.990783243 |
\( \frac{37525044319}{2197000} a - \frac{7169596274}{274625} \) |
\( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( 104 i - 146\) , \( -666 i + 546\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(104i-146\right){x}-666i+546$ |
| 37570.12-b2 |
37570.12-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.12 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{6} \cdot 5^{3} \cdot 13^{3} \cdot 17^{6} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.699031126$ |
2.097093378 |
\( \frac{37525044319}{2197000} a - \frac{7169596274}{274625} \) |
\( \bigl[1\) , \( -i\) , \( i\) , \( 179 i + 6\) , \( 658 i + 757\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(179i+6\right){x}+658i+757$ |
| 42250.6-f2 |
42250.6-f |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.6 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{6} \cdot 5^{9} \cdot 13^{9} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.357490328$ |
2.144941969 |
\( \frac{37525044319}{2197000} a - \frac{7169596274}{274625} \) |
\( \bigl[i\) , \( -i\) , \( 1\) , \( -574 i - 379\) , \( 7251 i + 374\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(-574i-379\right){x}+7251i+374$ |
| 66560.4-k2 |
66560.4-k |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
66560.4 |
\( 2^{10} \cdot 5 \cdot 13 \) |
\( 2^{36} \cdot 5^{3} \cdot 13^{3} \) |
$2.87059$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.509502108$ |
1.528506326 |
\( \frac{37525044319}{2197000} a - \frac{7169596274}{274625} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -148 i - 304\) , \( 1724 i + 1932\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(-148i-304\right){x}+1724i+1932$ |
| 66560.4-p2 |
66560.4-p |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
66560.4 |
\( 2^{10} \cdot 5 \cdot 13 \) |
\( 2^{36} \cdot 5^{3} \cdot 13^{3} \) |
$2.87059$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.509502108$ |
1.528506326 |
\( \frac{37525044319}{2197000} a - \frac{7169596274}{274625} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 148 i + 304\) , \( 1932 i - 1724\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(148i+304\right){x}+1932i-1724$ |
| 83200.6-i2 |
83200.6-i |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.6 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{30} \cdot 5^{9} \cdot 13^{3} \) |
$3.03528$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.322237427$ |
1.933424563 |
\( \frac{37525044319}{2197000} a - \frac{7169596274}{274625} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -754 i - 385\) , \( 9773 i - 503\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-754i-385\right){x}+9773i-503$ |
*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.
