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
5202.5-i3
5202.5-i
$8$
$16$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
5202.5
\( 2 \cdot 3^{2} \cdot 17^{2} \)
\( 2 \cdot 3^{2} \cdot 17^{20} \)
$2.14648$
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2^{6} \)
$1$
$0.091877073$
4.157881714
\( \frac{61437923106397764191713}{291967151254001210886} a - \frac{146204680417750243067160}{48661191875666868481} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -4305 a - 924\) , \( 137739 a - 127314\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(-4305a-924\right){x}+137739a-127314$
41616.5-g3
41616.5-g
$8$
$16$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
41616.5
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \)
\( 2^{13} \cdot 3^{2} \cdot 17^{20} \)
$3.60993$
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{8} \)
$3.826981769$
$0.045938536$
3.978034379
\( \frac{61437923106397764191713}{291967151254001210886} a - \frac{146204680417750243067160}{48661191875666868481} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( -17220 a - 3696\) , \( 1101912 a - 1018512\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-17220a-3696\right){x}+1101912a-1018512$
46818.8-k3
46818.8-k
$8$
$16$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
46818.8
\( 2 \cdot 3^{4} \cdot 17^{2} \)
\( 2 \cdot 3^{14} \cdot 17^{20} \)
$3.71781$
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{5} \)
$13.65003097$
$0.030625691$
4.729601183
\( \frac{61437923106397764191713}{291967151254001210886} a - \frac{146204680417750243067160}{48661191875666868481} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -38745 a - 8316\) , \( -3718953 a + 3437478\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-38745a-8316\right){x}-3718953a+3437478$
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.