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-c1
28.1-c
$2$
$2$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( - 2^{8} \cdot 7^{3} \)
$1.49646$
$(-a-2), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$19.42800747$
1.334321031
\( -\frac{3528949}{686} a - \frac{20337669}{5488} \)
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 3 a + 6\) , \( 3 a + 7\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(3a+6\right){x}+3a+7$
196.2-b1
196.2-b
$2$
$2$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
196.2
\( 2^{2} \cdot 7^{2} \)
\( - 2^{8} \cdot 7^{9} \)
$2.43411$
$(-a-2), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$3.385530845$
$2.271514261$
4.225365669
\( -\frac{3528949}{686} a - \frac{20337669}{5488} \)
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -49 a - 157\) , \( -436 a - 1372\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-49a-157\right){x}-436a-1372$
1372.2-j1
1372.2-j
$2$
$2$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
1372.2
\( 2^{2} \cdot 7^{3} \)
\( - 2^{8} \cdot 7^{9} \)
$3.95927$
$(-a-2), (-a+3), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$0.976445967$
$10.94615819$
5.872621262
\( -\frac{3528949}{686} a - \frac{20337669}{5488} \)
\( \bigl[1\) , \( 0\) , \( a\) , \( 5 a - 35\) , \( -16 a + 78\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(5a-35\right){x}-16a+78$
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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.