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
20.2-a1
20.2-a
$2$
$2$
\(\Q(\sqrt{11}) \)
$2$
$[2, 0]$
20.2
\( 2^{2} \cdot 5 \)
\( 2^{8} \cdot 5^{2} \)
$1.25349$
$(a+3), (-a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \cdot 3 \)
$1$
$7.019918163$
1.587438723
\( \frac{12288}{25} a - \frac{28672}{25} \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 12 a + 46\) , \( -82 a - 269\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(12a+46\right){x}-82a-269$
20.2-a2
20.2-a
$2$
$2$
\(\Q(\sqrt{11}) \)
$2$
$[2, 0]$
20.2
\( 2^{2} \cdot 5 \)
\( 2^{4} \cdot 5 \)
$1.25349$
$(a+3), (-a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 3 \)
$1$
$14.03983632$
1.587438723
\( -\frac{9052192}{5} a + \frac{30047888}{5} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( a - 13\) , \( 7 a - 28\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-13\right){x}+7a-28$
20.2-b1
20.2-b
$2$
$2$
\(\Q(\sqrt{11}) \)
$2$
$[2, 0]$
20.2
\( 2^{2} \cdot 5 \)
\( 2^{8} \cdot 5^{2} \)
$1.25349$
$(a+3), (-a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$24.21146987$
1.825008208
\( \frac{12288}{25} a - \frac{28672}{25} \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 12 a + 46\) , \( 82 a + 269\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(12a+46\right){x}+82a+269$
20.2-b2
20.2-b
$2$
$2$
\(\Q(\sqrt{11}) \)
$2$
$[2, 0]$
20.2
\( 2^{2} \cdot 5 \)
\( 2^{4} \cdot 5 \)
$1.25349$
$(a+3), (-a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 1 \)
$1$
$48.42293974$
1.825008208
\( -\frac{9052192}{5} a + \frac{30047888}{5} \)
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 3 a - 9\) , \( -2 a + 8\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(3a-9\right){x}-2a+8$
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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.