| 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 |
| 16900.6-a1 |
16900.6-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16900.6 |
\( 2^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{9} \cdot 13^{3} \) |
$2.03770$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.143102817$ |
2.286205634 |
\( -\frac{47255552}{3125} a - \frac{92655616}{3125} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 68 i + 10\) , \( -142 i - 169\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(68i+10\right){x}-142i-169$ |
| 67600.6-c1 |
67600.6-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{9} \cdot 13^{9} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.317039678$ |
0.634079357 |
\( -\frac{47255552}{3125} a - \frac{92655616}{3125} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 456 i - 758\) , \( 8016 i - 7137\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(456i-758\right){x}+8016i-7137$ |
| 84500.6-e1 |
84500.6-e |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.6 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{15} \cdot 13^{9} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.141784454$ |
1.701413454 |
\( -\frac{47255552}{3125} a - \frac{92655616}{3125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1662 i + 4101\) , \( -98350 i + 60812\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(1662i+4101\right){x}-98350i+60812$ |
| 84500.9-d1 |
84500.9-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.9 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{15} \cdot 13^{9} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.141784454$ |
1.417844545 |
\( -\frac{47255552}{3125} a - \frac{92655616}{3125} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( -4402 i + 447\) , \( 69501 i - 94091\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+\left(-4402i+447\right){x}+69501i-94091$ |
*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.
