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
1024.1-a1
1024.1-a
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1024.1
\( 2^{10} \)
\( 2^{12} \)
$0.87554$
$(2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$6.875185818$
0.992347595
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)
${y}^2={x}^{3}-{x}$
1024.1-a2
1024.1-a
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1024.1
\( 2^{10} \)
\( 2^{24} \)
$0.87554$
$(2)$
0
$\Z/4\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 2^{2} \)
$1$
$3.437592909$
0.992347595
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \)
${y}^2={x}^{3}+4{x}$
1024.1-a3
1024.1-a
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1024.1
\( 2^{10} \)
\( 2^{18} \)
$0.87554$
$(2)$
0
$\Z/2\Z$
$\textsf{potential}$
$-16$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 1 \)
$1$
$3.437592909$
0.992347595
\( 287496 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( -14\bigr] \)
${y}^2={x}^{3}-11{x}-14$
1024.1-a4
1024.1-a
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1024.1
\( 2^{10} \)
\( 2^{18} \)
$0.87554$
$(2)$
0
$\Z/4\Z$
$\textsf{potential}$
$-16$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 2^{2} \)
$1$
$3.437592909$
0.992347595
\( 287496 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( 14\bigr] \)
${y}^2={x}^{3}-11{x}+14$
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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.