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
113.1-a1
113.1-a
$4$
$4$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
113.1
\( 113 \)
\( - 113^{4} \)
$1.37536$
$(-3a^2-a+8)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$4.807463618$
0.686780516
\( -\frac{807377140974525125}{163047361} a^{2} + \frac{448068448385987525}{163047361} a + \frac{1814165677886203758}{163047361} \)
\( \bigl[a^{2} + a - 2\) , \( a^{2} - 2\) , \( a\) , \( 175 a^{2} - 99 a - 400\) , \( 1306 a^{2} - 733 a - 2948\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(175a^{2}-99a-400\right){x}+1306a^{2}-733a-2948$
113.1-a2
113.1-a
$4$
$4$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
113.1
\( 113 \)
\( 113 \)
$1.37536$
$(-3a^2-a+8)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$19.22985447$
0.686780516
\( \frac{10689425113170560565}{113} a^{2} - \frac{24018920204699885365}{113} a + \frac{8572253372285048258}{113} \)
\( \bigl[a^{2} + a - 2\) , \( a^{2} - 2\) , \( a\) , \( 5 a^{2} + 11 a - 50\) , \( -54 a^{2} + 85 a + 28\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(5a^{2}+11a-50\right){x}-54a^{2}+85a+28$
113.1-a3
113.1-a
$4$
$4$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
113.1
\( 113 \)
\( 113^{2} \)
$1.37536$
$(-3a^2-a+8)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$38.45970894$
0.686780516
\( \frac{1728506301750}{12769} a^{2} - \frac{3884911356975}{12769} a + \frac{1387967352157}{12769} \)
\( \bigl[a^{2} + a - 2\) , \( a^{2} - 2\) , \( a\) , \( 10 a^{2} - 4 a - 25\) , \( 16 a^{2} - 8 a - 38\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(10a^{2}-4a-25\right){x}+16a^{2}-8a-38$
113.1-a4
113.1-a
$4$
$4$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
113.1
\( 113 \)
\( 113 \)
$1.37536$
$(-3a^2-a+8)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$76.91941789$
0.686780516
\( \frac{639685}{113} a^{2} - \frac{1302810}{113} a + \frac{452313}{113} \)
\( \bigl[a^{2} + a - 2\) , \( a^{2} - 2\) , \( a\) , \( a\) , \( a^{2} - 2\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+a{x}+a^{2}-2$
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.