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
1521.1-a1
1521.1-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
1521.1
\( 3^{2} \cdot 13^{2} \)
\( 3^{2} \cdot 13^{2} \)
$1.47645$
$(3), (13)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 1 \)
$1.106436642$
$7.561180171$
3.162038233
\( \frac{12167}{39} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}+{x}$
1521.1-a2
1521.1-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
1521.1
\( 3^{2} \cdot 13^{2} \)
\( 3^{4} \cdot 13^{4} \)
$1.47645$
$(3), (13)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$2.212873284$
$3.780590085$
3.162038233
\( \frac{10218313}{1521} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( -4\) , \( -5\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}-4{x}-5$
1521.1-a3
1521.1-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
1521.1
\( 3^{2} \cdot 13^{2} \)
\( 3^{2} \cdot 13^{8} \)
$1.47645$
$(3), (13)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$4.425746569$
$1.890295042$
3.162038233
\( \frac{822656953}{85683} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( -19\) , \( 22\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}-19{x}+22$
1521.1-a4
1521.1-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
1521.1
\( 3^{2} \cdot 13^{2} \)
\( 3^{8} \cdot 13^{2} \)
$1.47645$
$(3), (13)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1.106436642$
$1.890295042$
3.162038233
\( \frac{37159393753}{1053} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( -69\) , \( -252\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}-69{x}-252$
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Pari/GP
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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.