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
124.1-a1
124.1-a
$3$
$25$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
124.1
\( 2^{2} \cdot 31 \)
\( 2^{50} \cdot 31 \)
$0.51648$
$(-6a+1), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.2
$1$
\( 1 \)
$1$
$0.368431786$
0.425428381
\( -\frac{936087656892551}{1040187392} a + \frac{51401239062153}{520093696} \)
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 1300 a - 550\) , \( -9800 a - 7280\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(1300a-550\right){x}-9800a-7280$
124.1-a2
124.1-a
$3$
$25$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
124.1
\( 2^{2} \cdot 31 \)
\( 2^{2} \cdot 31 \)
$0.51648$
$(-6a+1), (2)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.1
$1$
\( 1 \)
$1$
$9.210794651$
0.425428381
\( -\frac{24551}{62} a + \frac{45753}{31} \)
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 0\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}$
124.1-a3
124.1-a
$3$
$25$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
124.1
\( 2^{2} \cdot 31 \)
\( 2^{10} \cdot 31^{5} \)
$0.51648$
$(-6a+1), (2)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5Cs.1.1
$1$
\( 5 \)
$1$
$1.842158930$
0.425428381
\( \frac{511363962461}{916132832} a + \frac{1018073036305}{916132832} \)
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -15 a + 5\) , \( -7 a + 21\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-15a+5\right){x}-7a+21$
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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.