| 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 |
| 2610.3-a1 |
2610.3-a |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2610.3 |
\( 2 \cdot 3^{2} \cdot 5 \cdot 29 \) |
\( 2^{5} \cdot 3^{2} \cdot 5^{10} \cdot 29^{2} \) |
$1.27741$ |
$(a+1), (2a+1), (-2a+5), (3)$ |
$1$ |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$1.103989287$ |
$1.041549501$ |
2.299718986 |
\( -\frac{4595304741012881}{197109375000} a - \frac{8721492355789967}{197109375000} \) |
\( \bigl[i\) , \( -i - 1\) , \( i + 1\) , \( -58 i - 66\) , \( -240 i - 148\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-58i-66\right){x}-240i-148$ |
| 2610.3-a2 |
2610.3-a |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2610.3 |
\( 2 \cdot 3^{2} \cdot 5 \cdot 29 \) |
\( 2 \cdot 3^{10} \cdot 5^{2} \cdot 29^{10} \) |
$1.27741$ |
$(a+1), (2a+1), (-2a+5), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2^{2} \) |
$5.519946439$ |
$0.208309900$ |
2.299718986 |
\( -\frac{35923163098529556606799}{5111592884597442150} a - \frac{94467494734601586476593}{5111592884597442150} \) |
\( \bigl[1\) , \( i + 1\) , \( i + 1\) , \( 1447 i + 1148\) , \( -6426 i + 30903\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(1447i+1148\right){x}-6426i+30903$ |
| 2610.3-a3 |
2610.3-a |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2610.3 |
\( 2 \cdot 3^{2} \cdot 5 \cdot 29 \) |
\( 2^{2} \cdot 3^{20} \cdot 5 \cdot 29^{5} \) |
$1.27741$ |
$(a+1), (2a+1), (-2a+5), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2^{2} \) |
$2.759973219$ |
$0.416619800$ |
2.299718986 |
\( \frac{15657570839651791}{12111628373010} a - \frac{170997651070168}{2018604728835} \) |
\( \bigl[i\) , \( -i - 1\) , \( i + 1\) , \( 232 i - 66\) , \( 1808 i - 42\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(232i-66\right){x}+1808i-42$ |
| 2610.3-a4 |
2610.3-a |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2610.3 |
\( 2 \cdot 3^{2} \cdot 5 \cdot 29 \) |
\( 2^{10} \cdot 3^{4} \cdot 5^{5} \cdot 29 \) |
$1.27741$ |
$(a+1), (2a+1), (-2a+5), (3)$ |
$1$ |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$0.551994643$ |
$2.083099003$ |
2.299718986 |
\( -\frac{10059024449}{26100000} a + \frac{43710667}{271875} \) |
\( \bigl[1\) , \( i + 1\) , \( i + 1\) , \( 2 i - 7\) , \( 11 i - 8\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(2i-7\right){x}+11i-8$ |
*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.
