| 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 |
| 225.2-a2 |
225.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
225.2 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{20} \) |
$0.69217$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.558925428$ |
0.558925428 |
\( \frac{117751185817608007}{457763671875} a - \frac{2360548126387992}{152587890625} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( 105 i + 396\) , \( -2982 i + 1054\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}+\left(105i+396\right){x}-2982i+1054$ |
| 2025.2-c2 |
2025.2-c |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2025.2 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{14} \cdot 5^{20} \) |
$1.19888$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.300312843$ |
$0.186308476$ |
1.938074434 |
\( \frac{117751185817608007}{457763671875} a - \frac{2360548126387992}{152587890625} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( 945 i + 3555\) , \( 79569 i - 32008\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}+\left(945i+3555\right){x}+79569i-32008$ |
| 5625.3-b2 |
5625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5625.3 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{32} \) |
$1.54774$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.111785085$ |
1.788561370 |
\( \frac{117751185817608007}{457763671875} a - \frac{2360548126387992}{152587890625} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( 2625 i + 9875\) , \( -367500 i + 151477\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(2625i+9875\right){x}-367500i+151477$ |
| 18000.2-b2 |
18000.2-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
18000.2 |
\( 2^{4} \cdot 3^{2} \cdot 5^{3} \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{26} \) |
$2.07008$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$3.063921427$ |
$0.124979525$ |
3.063419561 |
\( \frac{117751185817608007}{457763671875} a - \frac{2360548126387992}{152587890625} \) |
\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( 7579 i + 3060\) , \( 63243 i + 277817\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(7579i+3060\right){x}+63243i+277817$ |
| 18000.3-a2 |
18000.3-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
18000.3 |
\( 2^{4} \cdot 3^{2} \cdot 5^{3} \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{26} \) |
$2.07008$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$3.063921427$ |
$0.124979525$ |
3.063419561 |
\( \frac{117751185817608007}{457763671875} a - \frac{2360548126387992}{152587890625} \) |
\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( -5061 i + 6420\) , \( 156987 i + 237775\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-5061i+6420\right){x}+156987i+237775$ |
| 50625.3-b2 |
50625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{14} \cdot 5^{32} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$2.400975354$ |
$0.037261695$ |
2.862861179 |
\( \frac{117751185817608007}{457763671875} a - \frac{2360548126387992}{152587890625} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( 23625 i + 88871\) , \( 9922500 i - 4089872\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+\left(23625i+88871\right){x}+9922500i-4089872$ |
| 57600.2-g2 |
57600.2-g |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57600.2 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{20} \) |
$2.76869$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.139731357$ |
2.235701712 |
\( \frac{117751185817608007}{457763671875} a - \frac{2360548126387992}{152587890625} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( -1680 i - 6320\) , \( -80084 i - 187488\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(-1680i-6320\right){x}-80084i-187488$ |
| 65025.4-b2 |
65025.4-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65025.4 |
\( 3^{2} \cdot 5^{2} \cdot 17^{2} \) |
\( 3^{2} \cdot 5^{20} \cdot 17^{6} \) |
$2.85390$ |
$(-a-2), (2a+1), (a+4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.135559328$ |
2.168949249 |
\( \frac{117751185817608007}{457763671875} a - \frac{2360548126387992}{152587890625} \) |
\( \bigl[i\) , \( -i - 1\) , \( i\) , \( -4734 i - 5084\) , \( 205122 i + 96065\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-4734i-5084\right){x}+205122i+96065$ |
| 65025.6-b2 |
65025.6-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65025.6 |
\( 3^{2} \cdot 5^{2} \cdot 17^{2} \) |
\( 3^{2} \cdot 5^{20} \cdot 17^{6} \) |
$2.85390$ |
$(-a-2), (2a+1), (a-4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.135559328$ |
2.168949249 |
\( \frac{117751185817608007}{457763671875} a - \frac{2360548126387992}{152587890625} \) |
\( \bigl[i\) , \( i - 1\) , \( i\) , \( 1584 i - 6764\) , \( 71826 i - 207763\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(1584i-6764\right){x}+71826i-207763$ |
*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.
