| 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 |
| 78400.3-a1 |
78400.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
78400.3 |
\( 2^{6} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 5^{4} \cdot 7^{6} \) |
$2.58987$ |
$(3a-2), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.782661940$ |
1.807480327 |
\( \frac{1293836}{25} a - \frac{1028876}{25} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -56 a - 120\) , \( -448 a - 400\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-56a-120\right){x}-448a-400$ |
| 78400.3-a2 |
78400.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
78400.3 |
\( 2^{6} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 5^{2} \cdot 7^{6} \) |
$2.58987$ |
$(3a-2), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.565323880$ |
1.807480327 |
\( -\frac{5776}{5} a + 1728 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4 a - 20\) , \( -32 a + 32\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(4a-20\right){x}-32a+32$ |
| 78400.3-b1 |
78400.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
78400.3 |
\( 2^{6} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 5^{2} \cdot 7^{6} \) |
$2.58987$ |
$(3a-2), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.180292041$ |
$1.275729632$ |
3.477342639 |
\( -\frac{108}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a - 5\) , \( -40 a - 34\bigr] \) |
${y}^2={x}^{3}+\left(-3a-5\right){x}-40a-34$ |
| 78400.3-b2 |
78400.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
78400.3 |
\( 2^{6} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{22} \cdot 5^{4} \cdot 7^{6} \) |
$2.58987$ |
$(3a-2), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.360584082$ |
$0.637864816$ |
3.477342639 |
\( \frac{3721734}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -123 a - 205\) , \( -1160 a - 986\bigr] \) |
${y}^2={x}^{3}+\left(-123a-205\right){x}-1160a-986$ |
| 78400.3-c1 |
78400.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
78400.3 |
\( 2^{6} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 5^{2} \cdot 7^{6} \) |
$2.58987$ |
$(3a-2), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.565323880$ |
1.807480327 |
\( \frac{5776}{5} a + \frac{2864}{5} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -17 a - 2\) , \( 19 a - 21\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-17a-2\right){x}+19a-21$ |
| 78400.3-c2 |
78400.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
78400.3 |
\( 2^{6} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 5^{4} \cdot 7^{6} \) |
$2.58987$ |
$(3a-2), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.782661940$ |
1.807480327 |
\( -\frac{1293836}{25} a + \frac{52992}{5} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -77 a - 102\) , \( -585 a - 309\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-77a-102\right){x}-585a-309$ |
*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.
