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
11.1-a1
11.1-a
$3$
$25$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
11.1
\( 11 \)
\( 11^{2} \)
$1.52661$
$(7a-33)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.4.2
$1$
\( 2 \)
$0.915095465$
$8.512583687$
3.321593280
\( -\frac{52893159101157376}{11} \)
\( \bigl[0\) , \( -1\) , \( a + 1\) , \( -129410876 a - 606990812\) , \( 1735544452344 a + 8140425051145\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-129410876a-606990812\right){x}+1735544452344a+8140425051145$
11.1-a2
11.1-a
$3$
$25$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
11.1
\( 11 \)
\( 11^{10} \)
$1.52661$
$(7a-33)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5Cs.4.1
$1$
\( 2 \cdot 5 \)
$0.183019093$
$8.512583687$
3.321593280
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( -1\) , \( a + 1\) , \( -170996 a - 802042\) , \( 151040284 a + 708441725\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-170996a-802042\right){x}+151040284a+708441725$
11.1-a3
11.1-a
$3$
$25$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
11.1
\( 11 \)
\( 11^{2} \)
$1.52661$
$(7a-33)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.4.1
$1$
\( 2 \)
$0.915095465$
$8.512583687$
3.321593280
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( -1\) , \( a + 1\) , \( -5516 a - 25872\) , \( -1145176 a - 5371355\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-5516a-25872\right){x}-1145176a-5371355$
11.1-b1
11.1-b
$3$
$25$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
11.1
\( 11 \)
\( 11^{2} \)
$1.52661$
$(7a-33)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.2
$1$
\( 2 \)
$26.76114810$
$0.064435690$
0.735275139
\( -\frac{52893159101157376}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$
11.1-b2
11.1-b
$3$
$25$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
11.1
\( 11 \)
\( 11^{10} \)
$1.52661$
$(7a-33)$
$1$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5Cs.1.1
$1$
\( 2 \cdot 5 \)
$5.352229620$
$1.610892258$
0.735275139
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$
11.1-b3
11.1-b
$3$
$25$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
11.1
\( 11 \)
\( 11^{2} \)
$1.52661$
$(7a-33)$
$1$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.1
$1$
\( 2 \)
$1.070445924$
$40.27230645$
0.735275139
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}$
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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.