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
287.2-b2
287.2-b
$6$
$8$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
287.2
\( 7 \cdot 41 \)
\( 7^{4} \cdot 41^{4} \)
$1.60651$
$(-a^2-a+2), (3a^2-a-3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$12.61392259$
0.900994471
\( \frac{2192037233085291}{138462289} a^{2} + \frac{2267219548655833}{138462289} a - \frac{566434328572957}{138462289} \)
\( \bigl[a^{2} - 2\) , \( -a^{2} - a + 2\) , \( a^{2} - 1\) , \( 26 a^{2} - 46 a - 102\) , \( 179 a^{2} - 200 a - 526\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(26a^{2}-46a-102\right){x}+179a^{2}-200a-526$
2009.3-d5
2009.3-d
$6$
$8$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
2009.3
\( 7^{2} \cdot 41 \)
\( 7^{10} \cdot 41^{4} \)
$2.22194$
$(-a^2-a+2), (3a^2-a-3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$18.63210072$
1.330864337
\( \frac{2192037233085291}{138462289} a^{2} + \frac{2267219548655833}{138462289} a - \frac{566434328572957}{138462289} \)
\( \bigl[a^{2} + a - 1\) , \( 0\) , \( 0\) , \( -131 a^{2} - 99 a + 3\) , \( 1047 a^{2} + 1119 a - 495\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}={x}^{3}+\left(-131a^{2}-99a+3\right){x}+1047a^{2}+1119a-495$
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.