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
$3$
$25$
\(\Q(\sqrt{65}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{2} \)
$2.38941$
$(11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.2
$1$
\( 1 \)
$43.97937822$
$0.064435690$
0.702989580
\( -\frac{52893159101157376}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$
121.1-a2
121.1-a
$3$
$25$
\(\Q(\sqrt{65}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{10} \)
$2.38941$
$(11)$
$1$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5Cs.1.1
$1$
\( 5 \)
$8.795875644$
$1.610892258$
0.702989580
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$
121.1-a3
121.1-a
$3$
$25$
\(\Q(\sqrt{65}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{2} \)
$2.38941$
$(11)$
$1$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.1
$1$
\( 1 \)
$1.759175128$
$40.27230645$
0.702989580
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}$
121.1-b1
121.1-b
$3$
$25$
\(\Q(\sqrt{65}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 2^{12} \cdot 11^{2} \)
$2.38941$
$(11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.3
$25$
\( 1 \)
$32.12215141$
$0.064435690$
12.83643531
\( -\frac{52893159101157376}{11} \)
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( -70382 a - 250245\) , \( -20366022 a - 71943939\bigr] \)
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-70382a-250245\right){x}-20366022a-71943939$
121.1-b2
121.1-b
$3$
$25$
\(\Q(\sqrt{65}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 2^{12} \cdot 11^{10} \)
$2.38941$
$(11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5Cs.1.3
$1$
\( 5 \)
$6.424430282$
$1.610892258$
12.83643531
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( -92 a - 325\) , \( -1612 a - 5699\bigr] \)
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-92a-325\right){x}-1612a-5699$
121.1-b3
121.1-b
$3$
$25$
\(\Q(\sqrt{65}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 2^{12} \cdot 11^{2} \)
$2.38941$
$(11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.4
$1$
\( 1 \)
$1.284886056$
$40.27230645$
12.83643531
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( -2 a - 5\) , \( 18 a + 61\bigr] \)
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a-5\right){x}+18a+61$
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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.