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
$3$
$25$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
11.1
\( 11 \)
\( 11^{2} \)
$2.35266$
$(70a+471)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.2
$1$
\( 2 \)
$58.18256016$
$0.064435690$
1.037304259
\( -\frac{52893159101157376}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$
11.1-a2
11.1-a
$3$
$25$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
11.1
\( 11 \)
\( 11^{10} \)
$2.35266$
$(70a+471)$
$1$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5Cs.1.1
$1$
\( 2 \cdot 5 \)
$11.63651203$
$1.610892258$
1.037304259
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$
11.1-a3
11.1-a
$3$
$25$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
11.1
\( 11 \)
\( 11^{2} \)
$2.35266$
$(70a+471)$
$1$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.1
$1$
\( 2 \)
$2.327302406$
$40.27230645$
1.037304259
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}$
11.1-b1
11.1-b
$3$
$25$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
11.1
\( 11 \)
\( 11^{2} \)
$2.35266$
$(70a+471)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.4.2
$1$
\( 2 \)
$5.612837583$
$8.512583687$
13.21997756
\( -\frac{52893159101157376}{11} \)
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 4688891060561 a - 36237701385816\) , \( -14859019779017908422 a + 114836688394705117771\bigr] \)
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4688891060561a-36237701385816\right){x}-14859019779017908422a+114836688394705117771$
11.1-b2
11.1-b
$3$
$25$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
11.1
\( 11 \)
\( 11^{10} \)
$2.35266$
$(70a+471)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5Cs.4.1
$1$
\( 2 \cdot 5 \)
$1.122567516$
$8.512583687$
13.21997756
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -6195627759 a - 41686761846\) , \( 1292706345403712 a + 8697866248261405\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6195627759a-41686761846\right){x}+1292706345403712a+8697866248261405$
11.1-b3
11.1-b
$3$
$25$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
11.1
\( 11 \)
\( 11^{2} \)
$2.35266$
$(70a+471)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.4.1
$1$
\( 2 \)
$5.612837583$
$8.512583687$
13.21997756
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 199858961 a - 1544593196\) , \( 9820121401118 a - 75893984805809\bigr] \)
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(199858961a-1544593196\right){x}+9820121401118a-75893984805809$
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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.