| 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 |
| 45.1-a4 |
45.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$1.46377$ |
$(5,a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.148891872$ |
$2.235701712$ |
1.519247123 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$ |
| 45.1-b4 |
45.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{8} \cdot 5^{8} \) |
$1.46377$ |
$(5,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$2.235701712$ |
1.413981916 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -38\) , \( 78\bigr] \) |
${y}^2+a{x}{y}={x}^3-38{x}+78$ |
| 405.1-a4 |
405.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 2^{12} \cdot 3^{20} \cdot 5^{8} \) |
$2.53532$ |
$(5,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.745233904$ |
1.885309221 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -355\) , \( -1037\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-355{x}-1037$ |
| 405.1-b4 |
405.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{20} \cdot 5^{8} \) |
$2.53532$ |
$(5,a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$5.036899059$ |
$0.745233904$ |
4.748056122 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -90\) , \( 175\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-90{x}+175$ |
| 720.1-c4 |
720.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{8} \cdot 5^{8} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$1.117850856$ |
2.827963832 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -36\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2-36{x}$ |
| 720.1-f4 |
720.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
720.1 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{24} \cdot 3^{8} \cdot 5^{8} \) |
$2.92753$ |
$(2,a), (5,a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$3.714905803$ |
$1.117850856$ |
5.252809626 |
\( \frac{111284641}{50625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -160\) , \( 308\bigr] \) |
${y}^2={x}^3+{x}^2-160{x}+308$ |
*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.
