| 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-a3 |
130.4-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
130.4 |
\( 2 \cdot 5 \cdot 13 \) |
\( 2^{3} \cdot 5^{6} \cdot 13^{6} \) |
$0.60347$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.441089584$ |
0.480363194 |
\( \frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \) |
\( \bigl[i\) , \( i + 1\) , \( i\) , \( i + 15\) , \( -30 i + 30\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(i+15\right){x}-30i+30$ |
| 5200.6-b3 |
5200.6-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5200.6 |
\( 2^{4} \cdot 5^{2} \cdot 13 \) |
\( 2^{15} \cdot 5^{12} \cdot 13^{6} \) |
$1.51764$ |
$(a+1), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \) |
$0.879173796$ |
$0.322237427$ |
2.266421617 |
\( \frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -229 i + 184\) , \( -2832 i - 2761\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-229i+184\right){x}-2832i-2761$ |
| 8450.9-a3 |
8450.9-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8450.9 |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{3} \cdot 5^{12} \cdot 13^{12} \) |
$1.71349$ |
$(a+1), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \) |
$1.365868524$ |
$0.178745164$ |
1.953139148 |
\( \frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \) |
\( \bigl[i\) , \( i\) , \( 0\) , \( -266 i - 915\) , \( 19254 i + 12233\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+i{x}^{2}+\left(-266i-915\right){x}+19254i+12233$ |
| 10530.4-a3 |
10530.4-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
10530.4 |
\( 2 \cdot 3^{4} \cdot 5 \cdot 13 \) |
\( 2^{3} \cdot 3^{12} \cdot 5^{6} \cdot 13^{6} \) |
$1.81040$ |
$(a+1), (2a+1), (2a+3), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$1$ |
$0.480363194$ |
2.882179168 |
\( \frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \) |
\( \bigl[1\) , \( -1\) , \( i\) , \( 4 i + 132\) , \( -947 i + 678\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}-{x}^{2}+\left(4i+132\right){x}-947i+678$ |
| 13520.6-c3 |
13520.6-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{15} \cdot 5^{6} \cdot 13^{12} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.199843168$ |
2.398118025 |
\( \frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -714 i - 269\) , \( -11042 i + 12328\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-714i-269\right){x}-11042i+12328$ |
| 16250.6-l3 |
16250.6-l |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.6 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{3} \cdot 5^{18} \cdot 13^{6} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.288217916$ |
3.458615002 |
\( \frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \) |
\( \bigl[1\) , \( i - 1\) , \( 0\) , \( 12 i + 366\) , \( 4498 i - 3386\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(12i+366\right){x}+4498i-3386$ |
| 16640.4-g3 |
16640.4-g |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16640.4 |
\( 2^{8} \cdot 5 \cdot 13 \) |
\( 2^{27} \cdot 5^{6} \cdot 13^{6} \) |
$2.02982$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.360272396$ |
2.161634376 |
\( \frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -8 i - 234\) , \( -1682 i - 2164\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-8i-234\right){x}-1682i-2164$ |
| 26000.4-g3 |
26000.4-g |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{15} \cdot 5^{12} \cdot 13^{6} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$0.078905109$ |
$0.322237427$ |
3.661369868 |
\( \frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 240 i + 168\) , \( 1808 i + 3600\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(240i+168\right){x}+1808i+3600$ |
| 37570.10-c3 |
37570.10-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.10 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{3} \cdot 5^{6} \cdot 13^{6} \cdot 17^{6} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.476117985$ |
$0.349515563$ |
5.990783243 |
\( \frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \) |
\( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( -126 i - 216\) , \( -2996 i - 716\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-126i-216\right){x}-2996i-716$ |
| 37570.12-b3 |
37570.12-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.12 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{3} \cdot 5^{6} \cdot 13^{6} \cdot 17^{6} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.349515563$ |
2.097093378 |
\( \frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \) |
\( \bigl[1\) , \( -i\) , \( i\) , \( 109 i - 224\) , \( -194 i + 3077\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(109i-224\right){x}-194i+3077$ |
| 42250.6-f3 |
42250.6-f |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.6 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{3} \cdot 5^{12} \cdot 13^{12} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.178745164$ |
2.144941969 |
\( \frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \) |
\( \bigl[i\) , \( -i\) , \( 1\) , \( -804 i + 511\) , \( 13935 i + 17862\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(-804i+511\right){x}+13935i+17862$ |
| 66560.4-k3 |
66560.4-k |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
66560.4 |
\( 2^{10} \cdot 5 \cdot 13 \) |
\( 2^{33} \cdot 5^{6} \cdot 13^{6} \) |
$2.87059$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.254751054$ |
1.528506326 |
\( \frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -468 i + 16\) , \( -964 i + 7692\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(-468i+16\right){x}-964i+7692$ |
| 66560.4-p3 |
66560.4-p |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
66560.4 |
\( 2^{10} \cdot 5 \cdot 13 \) |
\( 2^{33} \cdot 5^{6} \cdot 13^{6} \) |
$2.87059$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.254751054$ |
1.528506326 |
\( \frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 468 i - 16\) , \( 7692 i + 964\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(468i-16\right){x}+7692i+964$ |
| 83200.6-i3 |
83200.6-i |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.6 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{27} \cdot 5^{12} \cdot 13^{6} \) |
$3.03528$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.161118713$ |
1.933424563 |
\( \frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -914 i + 735\) , \( 23565 i + 21353\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-914i+735\right){x}+23565i+21353$ |
*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.
