| 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 |
| 1690.1-a4 |
1690.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1690.1 |
\( 2 \cdot 5 \cdot 13^{2} \) |
\( 2^{5} \cdot 5^{2} \cdot 13^{3} \) |
$1.14588$ |
$(a+1), (-a-2), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$0.371035907$ |
$1.607133521$ |
1.192608490 |
\( \frac{12916359143}{200} a + \frac{17274394699}{200} \) |
\( \bigl[i\) , \( i\) , \( 0\) , \( -107 i + 21\) , \( -190 i + 420\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+i{x}^{2}+\left(-107i+21\right){x}-190i+420$ |
| 8450.1-b4 |
8450.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8450.1 |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{5} \cdot 5^{8} \cdot 13^{9} \) |
$1.71349$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.199340379$ |
1.594723038 |
\( \frac{12916359143}{200} a + \frac{17274394699}{200} \) |
\( \bigl[1\) , \( i - 1\) , \( 1\) , \( 7071 i + 366\) , \( 147448 i + 171820\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(7071i+366\right){x}+147448i+171820$ |
| 13520.1-a4 |
13520.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.1 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{17} \cdot 5^{2} \cdot 13^{9} \) |
$1.92714$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.222869319$ |
0.891477279 |
\( \frac{12916359143}{200} a + \frac{17274394699}{200} \) |
\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( 3159 i + 4702\) , \( -101765 i + 128309\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(3159i+4702\right){x}-101765i+128309$ |
| 42250.7-l4 |
42250.7-l |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.7 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{5} \cdot 5^{8} \cdot 13^{9} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$0.199340379$ |
3.986807596 |
\( \frac{12916359143}{200} a + \frac{17274394699}{200} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -2332 i + 6686\) , \( -200700 i - 111192\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(-2332i+6686\right){x}-200700i-111192$ |
| 67600.1-f4 |
67600.1-f |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{17} \cdot 5^{8} \cdot 13^{3} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.359365980$ |
2.874927842 |
\( \frac{12916359143}{200} a + \frac{17274394699}{200} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( -941 i + 1965\) , \( -31012 i - 24461\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+\left(-941i+1965\right){x}-31012i-24461$ |
*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.
