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
28.1-c2
28.1-c
$2$
$2$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( - 2^{4} \cdot 7^{6} \)
$1.49646$
$(-a-2), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$9.714003739$
1.334321031
\( \frac{21413443562485}{235298} a + \frac{134478824713501}{470596} \)
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -17 a - 54\) , \( 31 a + 91\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-17a-54\right){x}+31a+91$
196.2-b2
196.2-b
$2$
$2$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
196.2
\( 2^{2} \cdot 7^{2} \)
\( - 2^{4} \cdot 7^{12} \)
$2.43411$
$(-a-2), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$6.771061691$
$1.135757130$
4.225365669
\( \frac{21413443562485}{235298} a + \frac{134478824713501}{470596} \)
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -789 a - 2477\) , \( -24112 a - 75716\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-789a-2477\right){x}-24112a-75716$
1372.2-j2
1372.2-j
$2$
$2$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
1372.2
\( 2^{2} \cdot 7^{3} \)
\( - 2^{4} \cdot 7^{12} \)
$3.95927$
$(-a-2), (-a+3), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1.952891934$
$5.473079098$
5.872621262
\( \frac{21413443562485}{235298} a + \frac{134478824713501}{470596} \)
\( \bigl[1\) , \( 0\) , \( a\) , \( -35 a - 55\) , \( 60 a + 802\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-35a-55\right){x}+60a+802$
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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.