| 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-a4 |
225.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
225.2 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$0.69217$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$8.942806850$ |
0.558925428 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$ |
| 2025.2-c4 |
2025.2-c |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2025.2 |
\( 3^{4} \cdot 5^{2} \) |
\( 3^{14} \cdot 5^{2} \) |
$1.19888$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.325078210$ |
$2.980935616$ |
1.938074434 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 0\) , \( -5\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-5$ |
| 5625.3-b4 |
5625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5625.3 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{14} \) |
$1.54774$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.788561370$ |
1.788561370 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 23\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}+23$ |
| 18000.2-b4 |
18000.2-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
18000.2 |
\( 2^{4} \cdot 3^{2} \cdot 5^{3} \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{8} \) |
$2.07008$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.191495089$ |
$1.999672402$ |
3.063419561 |
\( -\frac{1}{15} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -i\) , \( 16 i + 3\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}-i{x}+16i+3$ |
| 18000.3-a4 |
18000.3-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
18000.3 |
\( 2^{4} \cdot 3^{2} \cdot 5^{3} \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{8} \) |
$2.07008$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.191495089$ |
$1.999672402$ |
3.063419561 |
\( -\frac{1}{15} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( i + 1\) , \( -i\) , \( 16 i - 3\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}-i{x}+16i-3$ |
| 50625.3-b4 |
50625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50625.3 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{14} \cdot 5^{14} \) |
$2.68077$ |
$(-a-2), (2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.600243838$ |
$0.596187123$ |
2.862861179 |
\( -\frac{1}{15} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -4\) , \( 628\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-4{x}+628$ |
| 57600.2-g4 |
57600.2-g |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57600.2 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{2} \) |
$2.76869$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.235701712$ |
2.235701712 |
\( -\frac{1}{15} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 0\) , \( 12 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+12i$ |
| 65025.4-b4 |
65025.4-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65025.4 |
\( 3^{2} \cdot 5^{2} \cdot 17^{2} \) |
\( 3^{2} \cdot 5^{2} \cdot 17^{6} \) |
$2.85390$ |
$(-a-2), (2a+1), (a+4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.168949249$ |
2.168949249 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( i + 1\) , \( 1\) , \( i\) , \( 10 i - 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(i+1\right){x}^{2}+i{x}+10i-9$ |
| 65025.6-b4 |
65025.6-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65025.6 |
\( 3^{2} \cdot 5^{2} \cdot 17^{2} \) |
\( 3^{2} \cdot 5^{2} \cdot 17^{6} \) |
$2.85390$ |
$(-a-2), (2a+1), (a-4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.168949249$ |
2.168949249 |
\( -\frac{1}{15} \) |
\( \bigl[i\) , \( i - 1\) , \( i\) , \( -i + 1\) , \( 10 i + 9\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-i+1\right){x}+10i+9$ |
*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.
