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
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
1089.2
\( 3^{2} \cdot 11^{2} \)
\( 3^{24} \cdot 11^{2} \)
$1.35814$
$(-2a+3), (2a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \cdot 3 \)
$1$
$1.025585977$
2.325810380
\( \frac{9090072503}{5845851} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( 44\) , \( 55\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}+44{x}+55$
1089.2-a2
1089.2-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
1089.2
\( 3^{2} \cdot 11^{2} \)
\( 3^{12} \cdot 11^{4} \)
$1.35814$
$(-2a+3), (2a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{3} \cdot 3 \)
$1$
$2.051171954$
2.325810380
\( \frac{169112377}{88209} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( -11\) , \( 0\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}-11{x}$
1089.2-a3
1089.2-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
1089.2
\( 3^{2} \cdot 11^{2} \)
\( 3^{6} \cdot 11^{2} \)
$1.35814$
$(-2a+3), (2a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 3 \)
$1$
$4.102343908$
2.325810380
\( \frac{30664297}{297} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( -6\) , \( -9\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}-6{x}-9$
1089.2-a4
1089.2-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
1089.2
\( 3^{2} \cdot 11^{2} \)
\( 3^{6} \cdot 11^{8} \)
$1.35814$
$(-2a+3), (2a+1), (3)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{4} \cdot 3 \)
$1$
$1.025585977$
2.325810380
\( \frac{347873904937}{395307} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( -146\) , \( 621\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}-146{x}+621$
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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.