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
8.2-b1
8.2-b
$2$
$3$
\(\Q(\sqrt{129}) \)
$2$
$[2, 0]$
8.2
\( 2^{3} \)
\( - 2^{11} \)
$1.70689$
$(-a+6), (a+5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.2
$1$
\( 1 \)
$6.235527253$
$1.771317458$
1.944933359
\( -\frac{47232606203}{8} a - \frac{244609748133}{8} \)
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 17379 a - 107319\) , \( 2996015 a - 18512003\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(17379a-107319\right){x}+2996015a-18512003$
8.2-c1
8.2-c
$2$
$3$
\(\Q(\sqrt{129}) \)
$2$
$[2, 0]$
8.2
\( 2^{3} \)
\( - 2^{11} \)
$1.70689$
$(-a+6), (a+5)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.1
$1$
\( 3^{2} \)
$1$
$29.10944917$
2.562944090
\( -\frac{47232606203}{8} a - \frac{244609748133}{8} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -869257 a - 4501774\) , \( 1049040547 a + 5432884883\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-869257a-4501774\right){x}+1049040547a+5432884883$
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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.