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
49.2-b2
49.2-b
$2$
$7$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
49.2
\( 7^{2} \)
\( - 7^{3} \)
$1.72118$
$(-a-2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B
$1$
\( 2 \)
$0.214508932$
$18.74863282$
2.209718956
\( -4096 a + 16384 \)
\( \bigl[0\) , \( -1\) , \( a + 1\) , \( -2 a - 6\) , \( -6 a - 20\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2a-6\right){x}-6a-20$
49.2-c2
49.2-c
$2$
$7$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
49.2
\( 7^{2} \)
\( - 7^{9} \)
$1.72118$
$(-a-2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.2.1
$1$
\( 2 \)
$0.233677833$
$15.92365378$
2.044477338
\( -4096 a + 16384 \)
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 25 a - 98\) , \( -99 a + 401\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(25a-98\right){x}-99a+401$
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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.