| 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 |
| 10400.4-c2 |
10400.4-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
10400.4 |
\( 2^{5} \cdot 5^{2} \cdot 13 \) |
\( 2^{12} \cdot 5^{6} \cdot 13^{2} \) |
$1.80479$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.962588867$ |
1.962588867 |
\( \frac{54739584}{105625} a + \frac{278314688}{105625} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 12 i + 5\) , \( 7 i + 17\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(12i+5\right){x}+7i+17$ |
| 52000.4-g2 |
52000.4-g |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.4 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{12} \cdot 5^{12} \cdot 13^{2} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.301819801$ |
$0.877696423$ |
4.238498565 |
\( \frac{54739584}{105625} a + \frac{278314688}{105625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -58 i + 36\) , \( -8 i - 144\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-58i+36\right){x}-8i-144$ |
| 52000.6-c2 |
52000.6-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.6 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{12} \cdot 5^{12} \cdot 13^{2} \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.877696423$ |
1.755392847 |
\( \frac{54739584}{105625} a + \frac{278314688}{105625} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( -18 i - 66\) , \( -94 i - 108\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(-18i-66\right){x}-94i-108$ |
| 83200.4-k2 |
83200.4-k |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.4 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{12} \cdot 5^{6} \cdot 13^{2} \) |
$3.03528$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.635065254$ |
$1.962588867$ |
4.985487994 |
\( \frac{54739584}{105625} a + \frac{278314688}{105625} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -12 i - 5\) , \( -17 i + 7\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(-12i-5\right){x}-17i+7$ |
*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.
