| 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 |
| 578.1-c2 |
578.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2^{2} \cdot 17^{12} \) |
$2.14648$ |
$(-a+2), (17)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.245665415$ |
1.375183600 |
\( \frac{159661140625}{48275138} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -113\) , \( -329\bigr] \) |
${y}^2+{x}{y}={x}^{3}-113{x}-329$ |
| 578.1-d2 |
578.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
578.1 |
\( 2 \cdot 17^{2} \) |
\( 2^{2} \cdot 17^{12} \) |
$2.14648$ |
$(-a+2), (17)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$3.375774058$ |
$3.475148644$ |
1.596429988 |
\( \frac{159661140625}{48275138} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -2262 a - 5540\) , \( 62881 a + 154026\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-2262a-5540\right){x}+62881a+154026$ |
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*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.
