| 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-a4 |
130.4-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
130.4 |
\( 2 \cdot 5 \cdot 13 \) |
\( 2^{9} \cdot 5^{18} \cdot 13^{2} \) |
$0.60347$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.480363194$ |
0.480363194 |
\( -\frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \) |
\( \bigl[i\) , \( i + 1\) , \( i\) , \( -9 i - 130\) , \( 688 i - 882\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-9i-130\right){x}+688i-882$ |
| 5200.6-b4 |
5200.6-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5200.6 |
\( 2^{4} \cdot 5^{2} \cdot 13 \) |
\( 2^{21} \cdot 5^{24} \cdot 13^{2} \) |
$1.51764$ |
$(a+1), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$2.637521388$ |
$0.107412475$ |
2.266421617 |
\( -\frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( 1971 i - 1716\) , \( 86412 i + 51831\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(1971i-1716\right){x}+86412i+51831$ |
| 8450.9-a4 |
8450.9-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8450.9 |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{9} \cdot 5^{24} \cdot 13^{8} \) |
$1.71349$ |
$(a+1), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$4.097605573$ |
$0.059581721$ |
1.953139148 |
\( -\frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \) |
\( \bigl[i\) , \( i\) , \( 0\) , \( 2684 i + 8060\) , \( -553840 i - 196784\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+i{x}^{2}+\left(2684i+8060\right){x}-553840i-196784$ |
| 10530.4-a4 |
10530.4-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
10530.4 |
\( 2 \cdot 3^{4} \cdot 5 \cdot 13 \) |
\( 2^{9} \cdot 3^{12} \cdot 5^{18} \cdot 13^{2} \) |
$1.81040$ |
$(a+1), (2a+1), (2a+3), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{4} \) |
$1$ |
$0.160121064$ |
2.882179168 |
\( -\frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \) |
\( \bigl[1\) , \( -1\) , \( i\) , \( -86 i - 1173\) , \( 19834 i - 22731\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}-{x}^{2}+\left(-86i-1173\right){x}+19834i-22731$ |
| 13520.6-c4 |
13520.6-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{21} \cdot 5^{18} \cdot 13^{8} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.066614389$ |
2.398118025 |
\( -\frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( 6446 i + 2151\) , \( 208998 i - 367724\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(6446i+2151\right){x}+208998i-367724$ |
| 16250.6-l4 |
16250.6-l |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.6 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{9} \cdot 5^{30} \cdot 13^{2} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.096072638$ |
3.458615002 |
\( -\frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \) |
\( \bigl[1\) , \( i - 1\) , \( 0\) , \( -238 i - 3259\) , \( -92752 i + 107489\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-238i-3259\right){x}-92752i+107489$ |
| 16640.4-g4 |
16640.4-g |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16640.4 |
\( 2^{8} \cdot 5 \cdot 13 \) |
\( 2^{33} \cdot 5^{18} \cdot 13^{2} \) |
$2.02982$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.120090798$ |
2.161634376 |
\( -\frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 152 i + 2086\) , \( 54526 i + 46268\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(152i+2086\right){x}+54526i+46268$ |
| 26000.4-g4 |
26000.4-g |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{21} \cdot 5^{24} \cdot 13^{2} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$0.236715329$ |
$0.107412475$ |
3.661369868 |
\( -\frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -2200 i - 1412\) , \( -63800 i - 79056\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-2200i-1412\right){x}-63800i-79056$ |
| 37570.10-c4 |
37570.10-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.10 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{9} \cdot 5^{18} \cdot 13^{2} \cdot 17^{6} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{4} \) |
$0.158705995$ |
$0.116505187$ |
5.990783243 |
\( -\frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \) |
\( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( 1184 i + 1879\) , \( 78699 i - 744\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(1184i+1879\right){x}+78699i-744$ |
| 37570.12-b4 |
37570.12-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.12 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{9} \cdot 5^{18} \cdot 13^{2} \cdot 17^{6} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.116505187$ |
2.097093378 |
\( -\frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \) |
\( \bigl[1\) , \( -i\) , \( i\) , \( -901 i + 2031\) , \( -10607 i - 78368\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(-901i+2031\right){x}-10607i-78368$ |
| 42250.6-f4 |
42250.6-f |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.6 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{9} \cdot 5^{24} \cdot 13^{8} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.059581721$ |
2.144941969 |
\( -\frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \) |
\( \bigl[i\) , \( -i\) , \( 1\) , \( 6986 i - 4834\) , \( -450954 i - 375811\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(6986i-4834\right){x}-450954i-375811$ |
| 66560.4-k4 |
66560.4-k |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
66560.4 |
\( 2^{10} \cdot 5 \cdot 13 \) |
\( 2^{39} \cdot 5^{18} \cdot 13^{2} \) |
$2.87059$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{3} \) |
$1$ |
$0.084917018$ |
1.528506326 |
\( -\frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 4172 i - 304\) , \( -16516 i - 201588\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(4172i-304\right){x}-16516i-201588$ |
| 66560.4-p4 |
66560.4-p |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
66560.4 |
\( 2^{10} \cdot 5 \cdot 13 \) |
\( 2^{39} \cdot 5^{18} \cdot 13^{2} \) |
$2.87059$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.084917018$ |
1.528506326 |
\( -\frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -4172 i + 304\) , \( -201588 i + 16516\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-4172i+304\right){x}-201588i+16516$ |
| 83200.6-i4 |
83200.6-i |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.6 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{33} \cdot 5^{24} \cdot 13^{2} \) |
$3.03528$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{4} \) |
$1$ |
$0.053706237$ |
1.933424563 |
\( -\frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 7886 i - 6865\) , \( -699187 i - 407783\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(7886i-6865\right){x}-699187i-407783$ |
*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.
