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
$3$
$9$
\(\Q(\sqrt{73}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{2} \)
$2.53219$
$(11)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B
$1$
\( 1 \)
$1$
$3.020328858$
0.353502754
\( -\frac{69021696000}{11} a - \frac{260349952000}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10 a + 47\) , \( -16 a + 76\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}+\left(-10a+47\right){x}-16a+76$
121.1-a2
121.1-a
$3$
$9$
\(\Q(\sqrt{73}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{6} \)
$2.53219$
$(11)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3Cs
$1$
\( 1 \)
$1$
$3.020328858$
0.353502754
\( -\frac{4096000}{1331} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -1780000 a - 6714163\) , \( -3338142046 a - 12591478049\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}+\left(-1780000a-6714163\right){x}-3338142046a-12591478049$
121.1-a3
121.1-a
$3$
$9$
\(\Q(\sqrt{73}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{2} \)
$2.53219$
$(11)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B
$1$
\( 1 \)
$1$
$3.020328858$
0.353502754
\( \frac{69021696000}{11} a - \frac{329371648000}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( 10 a + 37\) , \( 16 a + 60\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}+\left(10a+37\right){x}+16a+60$
121.1-b1
121.1-b
$3$
$25$
\(\Q(\sqrt{73}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{2} \)
$2.53219$
$(11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.2
$1$
\( 1 \)
$27.02200633$
$0.064435690$
0.407579791
\( -\frac{52893159101157376}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$
121.1-b2
121.1-b
$3$
$25$
\(\Q(\sqrt{73}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{10} \)
$2.53219$
$(11)$
$1$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5Cs.1.1
$1$
\( 5 \)
$5.404401267$
$1.610892258$
0.407579791
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$
121.1-b3
121.1-b
$3$
$25$
\(\Q(\sqrt{73}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{2} \)
$2.53219$
$(11)$
$1$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.1
$1$
\( 1 \)
$1.080880253$
$40.27230645$
0.407579791
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}$
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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.