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
61504.3-a1
61504.3-a
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
61504.3
\( 2^{6} \cdot 31^{2} \)
\( 2^{22} \cdot 31^{7} \)
$2.43739$
$(6a-5), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2 \)
$1$
$0.504789498$
1.165761410
\( \frac{20086}{31} a - \frac{69202}{31} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( 94 a - 211\) , \( 833 a - 1518\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(94a-211\right){x}+833a-1518$
61504.3-b1
61504.3-b
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
61504.3
\( 2^{6} \cdot 31^{2} \)
\( 2^{22} \cdot 31^{3} \)
$2.43739$
$(6a-5), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$1$
$1.665014528$
3.845186344
\( 36 a - 38 \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 3 a - 6\) , \( 9 a - 31\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(3a-6\right){x}+9a-31$
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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.