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 |
6498.1-b3 |
6498.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6498.1 |
\( 2 \cdot 3^{2} \cdot 19^{2} \) |
\( 2^{12} \cdot 3^{6} \cdot 19^{2} \) |
$1.60459$ |
$(a+1), (3), (19)$ |
$0$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$2.429312260$ |
2.429312260 |
\( \frac{57066625}{32832} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -8\) , \( 0\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-8{x}$ |
58482.1-c3 |
58482.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
58482.1 |
\( 2 \cdot 3^{4} \cdot 19^{2} \) |
\( 2^{12} \cdot 3^{18} \cdot 19^{2} \) |
$2.77923$ |
$(a+1), (3), (19)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$0.690459601$ |
$0.809770753$ |
4.472911933 |
\( \frac{57066625}{32832} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( -72\) , \( 0\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}-72{x}$ |
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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.