| 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-a6 |
130.4-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
130.4 |
\( 2 \cdot 5 \cdot 13 \) |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
$0.60347$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$4.323268753$ |
0.480363194 |
\( \frac{4406742137}{8450} a + \frac{1310300809}{8450} \) |
\( \bigl[i\) , \( i + 1\) , \( i\) , \( 6 i - 5\) , \( -8 i\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(6i-5\right){x}-8i$ |
| 5200.6-b6 |
5200.6-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5200.6 |
\( 2^{4} \cdot 5^{2} \cdot 13 \) |
\( 2^{13} \cdot 5^{8} \cdot 13^{2} \) |
$1.51764$ |
$(a+1), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.293057932$ |
$0.966712281$ |
2.266421617 |
\( \frac{4406742137}{8450} a + \frac{1310300809}{8450} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( 151 i + 24\) , \( -440 i - 605\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(151i+24\right){x}-440i-605$ |
| 8450.9-a6 |
8450.9-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8450.9 |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
\( 2 \cdot 5^{8} \cdot 13^{8} \) |
$1.71349$ |
$(a+1), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.455289508$ |
$0.536235492$ |
1.953139148 |
\( \frac{4406742137}{8450} a + \frac{1310300809}{8450} \) |
\( \bigl[i\) , \( i\) , \( 0\) , \( -261 i + 425\) , \( 3077 i + 3197\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+i{x}^{2}+\left(-261i+425\right){x}+3077i+3197$ |
| 10530.4-a6 |
10530.4-a |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
10530.4 |
\( 2 \cdot 3^{4} \cdot 5 \cdot 13 \) |
\( 2 \cdot 3^{12} \cdot 5^{2} \cdot 13^{2} \) |
$1.81040$ |
$(a+1), (2a+1), (2a+3), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$1.441089584$ |
2.882179168 |
\( \frac{4406742137}{8450} a + \frac{1310300809}{8450} \) |
\( \bigl[1\) , \( -1\) , \( i\) , \( 49 i - 48\) , \( -218 i + 93\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}-{x}^{2}+\left(49i-48\right){x}-218i+93$ |
| 13520.6-c6 |
13520.6-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{13} \cdot 5^{2} \cdot 13^{8} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.599529506$ |
2.398118025 |
\( \frac{4406742137}{8450} a + \frac{1310300809}{8450} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( 146 i + 371\) , \( -2526 i + 1624\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(146i+371\right){x}-2526i+1624$ |
| 16250.6-l6 |
16250.6-l |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.6 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2 \cdot 5^{14} \cdot 13^{2} \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.864653750$ |
3.458615002 |
\( \frac{4406742137}{8450} a + \frac{1310300809}{8450} \) |
\( \bigl[1\) , \( i - 1\) , \( 0\) , \( 137 i - 134\) , \( 873 i - 386\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(137i-134\right){x}+873i-386$ |
| 16640.4-g6 |
16640.4-g |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16640.4 |
\( 2^{8} \cdot 5 \cdot 13 \) |
\( 2^{25} \cdot 5^{2} \cdot 13^{2} \) |
$2.02982$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.080817188$ |
2.161634376 |
\( \frac{4406742137}{8450} a + \frac{1310300809}{8450} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -88 i + 86\) , \( -162 i - 516\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-88i+86\right){x}-162i-516$ |
| 26000.4-g6 |
26000.4-g |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{13} \cdot 5^{8} \cdot 13^{2} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$0.236715329$ |
$0.966712281$ |
3.661369868 |
\( \frac{4406742137}{8450} a + \frac{1310300809}{8450} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -20 i - 152\) , \( 160 i + 664\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-20i-152\right){x}+160i+664$ |
| 37570.10-c6 |
37570.10-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.10 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2 \cdot 5^{2} \cdot 13^{2} \cdot 17^{6} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1.428353955$ |
$1.048546689$ |
5.990783243 |
\( \frac{4406742137}{8450} a + \frac{1310300809}{8450} \) |
\( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( -41 i + 124\) , \( -572 i - 217\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-41i+124\right){x}-572i-217$ |
| 37570.12-b6 |
37570.12-b |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.12 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2 \cdot 5^{2} \cdot 13^{2} \cdot 17^{6} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.048546689$ |
2.097093378 |
\( \frac{4406742137}{8450} a + \frac{1310300809}{8450} \) |
\( \bigl[1\) , \( -i\) , \( i\) , \( -126 i + 36\) , \( -225 i + 498\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(-126i+36\right){x}-225i+498$ |
| 42250.6-f6 |
42250.6-f |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.6 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2 \cdot 5^{8} \cdot 13^{8} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.536235492$ |
2.144941969 |
\( \frac{4406742137}{8450} a + \frac{1310300809}{8450} \) |
\( \bigl[i\) , \( -i\) , \( 1\) , \( 481 i + 131\) , \( 1536 i + 4119\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(481i+131\right){x}+1536i+4119$ |
| 66560.4-k6 |
66560.4-k |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
66560.4 |
\( 2^{10} \cdot 5 \cdot 13 \) |
\( 2^{31} \cdot 5^{2} \cdot 13^{2} \) |
$2.87059$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.764253163$ |
1.528506326 |
\( \frac{4406742137}{8450} a + \frac{1310300809}{8450} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 172 i + 176\) , \( -708 i + 1356\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(172i+176\right){x}-708i+1356$ |
| 66560.4-p6 |
66560.4-p |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
66560.4 |
\( 2^{10} \cdot 5 \cdot 13 \) |
\( 2^{31} \cdot 5^{2} \cdot 13^{2} \) |
$2.87059$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.764253163$ |
1.528506326 |
\( \frac{4406742137}{8450} a + \frac{1310300809}{8450} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -172 i - 176\) , \( 1356 i + 708\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-172i-176\right){x}+1356i+708$ |
| 83200.6-i6 |
83200.6-i |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.6 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{25} \cdot 5^{8} \cdot 13^{2} \) |
$3.03528$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.483356140$ |
1.933424563 |
\( \frac{4406742137}{8450} a + \frac{1310300809}{8450} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 606 i + 95\) , \( 2909 i + 4745\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(606i+95\right){x}+2909i+4745$ |
*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.
