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
$3$
$25$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{2} \)
$1.45191$
$(11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.2
$1$
\( 1 \)
$43.10278554$
$0.064435690$
1.133851549
\( -\frac{52893159101157376}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$
121.1-a2
121.1-a
$3$
$25$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{10} \)
$1.45191$
$(11)$
$1$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5Cs.1.1
$1$
\( 5 \)
$8.620557108$
$1.610892258$
1.133851549
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$
121.1-a3
121.1-a
$3$
$25$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{2} \)
$1.45191$
$(11)$
$1$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.1
$1$
\( 1 \)
$1.724111421$
$40.27230645$
1.133851549
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}$
121.1-b1
121.1-b
$3$
$25$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{2} \)
$1.45191$
$(11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.4.2
$1$
\( 1 \)
$0.915095465$
$8.512583687$
3.180183447
\( -\frac{52893159101157376}{11} \)
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 156406 a - 383194\) , \( -52884793 a + 129540991\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(156406a-383194\right){x}-52884793a+129540991$
121.1-b2
121.1-b
$3$
$25$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{10} \)
$1.45191$
$(11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5Cs.4.1
$1$
\( 5 \)
$0.183019093$
$8.512583687$
3.180183447
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 206 a - 504\) , \( -4823 a + 11811\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(206a-504\right){x}-4823a+11811$
121.1-b3
121.1-b
$3$
$25$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{2} \)
$1.45191$
$(11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.4.1
$1$
\( 1 \)
$0.915095465$
$8.512583687$
3.180183447
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( -6 a - 14\) , \( -28 a - 69\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a-14\right){x}-28a-69$
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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.