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
124.2-a1
124.2-a
$3$
$25$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
124.2
\( 2^{2} \cdot 31 \)
\( 2^{50} \cdot 31 \)
$0.51648$
$(6a-5), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.2
$1$
\( 1 \)
$1$
$0.368431786$
0.425428381
\( \frac{936087656892551}{1040187392} a - \frac{833285178768245}{1040187392} \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -1301 a + 751\) , \( 10550 a - 16530\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1301a+751\right){x}+10550a-16530$
124.2-a2
124.2-a
$3$
$25$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
124.2
\( 2^{2} \cdot 31 \)
\( 2^{2} \cdot 31 \)
$0.51648$
$(6a-5), (2)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.1
$1$
\( 1 \)
$1$
$9.210794651$
0.425428381
\( \frac{24551}{62} a + \frac{66955}{62} \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -a + 1\) , \( 0\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+1\right){x}$
124.2-a3
124.2-a
$3$
$25$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
124.2
\( 2^{2} \cdot 31 \)
\( 2^{10} \cdot 31^{5} \)
$0.51648$
$(6a-5), (2)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5Cs.1.1
$1$
\( 5 \)
$1$
$1.842158930$
0.425428381
\( -\frac{511363962461}{916132832} a + \frac{764718499383}{458066416} \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 14 a - 9\) , \( -3 a + 9\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(14a-9\right){x}-3a+9$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.