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
1089.2-a1
1089.2-a
$3$
$25$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1089.2
\( 3^{2} \cdot 11^{2} \)
\( 3^{6} \cdot 11^{2} \)
$1.85083$
$(-a), (11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.2
$1$
\( 1 \)
$13.84714261$
$0.427595683$
3.284367889
\( -\frac{52893159101157376}{11} \)
\( \bigl[0\) , \( a\) , \( 1\) , \( -7820 a - 23460\) , \( 1054319 a + 790739\bigr] \)
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-7820a-23460\right){x}+1054319a+790739$
1089.2-a2
1089.2-a
$3$
$25$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1089.2
\( 3^{2} \cdot 11^{2} \)
\( 3^{6} \cdot 11^{10} \)
$1.85083$
$(-a), (11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5Cs.4.1
$1$
\( 1 \)
$2.769428523$
$2.137978418$
3.284367889
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( a\) , \( 1\) , \( -10 a - 30\) , \( 79 a + 59\bigr] \)
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-10a-30\right){x}+79a+59$
1089.2-a3
1089.2-a
$3$
$25$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1089.2
\( 3^{2} \cdot 11^{2} \)
\( 3^{6} \cdot 11^{2} \)
$1.85083$
$(-a), (11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.1
$1$
\( 1 \)
$0.553885704$
$10.68989209$
3.284367889
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( a\) , \( 1\) , \( 0\) , \( -a - 1\bigr] \)
${y}^2+{y}={x}^{3}+a{x}^{2}-a-1$
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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.