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
121.1-a1
121.1-a
$3$
$25$
\(\Q(\sqrt{85}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 3^{12} \cdot 11^{2} \)
$2.73240$
$(11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.3
$25$
\( 1 \)
$16.70170261$
$0.064435690$
5.836436618
\( -\frac{52893159101157376}{11} \)
\( \bigl[0\) , \( a\) , \( 1\) , \( 86024 a - 445752\) , \( 29692976 a - 151922693\bigr] \)
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(86024a-445752\right){x}+29692976a-151922693$
121.1-a2
121.1-a
$3$
$25$
\(\Q(\sqrt{85}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 3^{12} \cdot 11^{10} \)
$2.73240$
$(11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5Cs.1.3
$1$
\( 5 \)
$3.340340522$
$1.610892258$
5.836436618
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( a\) , \( 1\) , \( 114 a - 582\) , \( 2436 a - 12473\bigr] \)
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(114a-582\right){x}+2436a-12473$
121.1-a3
121.1-a
$3$
$25$
\(\Q(\sqrt{85}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 3^{12} \cdot 11^{2} \)
$2.73240$
$(11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.4
$1$
\( 1 \)
$0.668068104$
$40.27230645$
5.836436618
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( a\) , \( 1\) , \( 4 a - 12\) , \( -24 a + 127\bigr] \)
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(4a-12\right){x}-24a+127$
121.1-b1
121.1-b
$3$
$25$
\(\Q(\sqrt{85}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{2} \)
$2.73240$
$(11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.2
$1$
\( 1 \)
$129.0533953$
$0.064435690$
1.803916594
\( -\frac{52893159101157376}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$
121.1-b2
121.1-b
$3$
$25$
\(\Q(\sqrt{85}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{10} \)
$2.73240$
$(11)$
$1$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5Cs.1.1
$1$
\( 5 \)
$25.81067907$
$1.610892258$
1.803916594
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$
121.1-b3
121.1-b
$3$
$25$
\(\Q(\sqrt{85}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{2} \)
$2.73240$
$(11)$
$1$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.1
$1$
\( 1 \)
$5.162135815$
$40.27230645$
1.803916594
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}$
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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.