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
2704.3-CMa1
2704.3-CMa
$1$
$1$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
2704.3
\( 2^{4} \cdot 13^{2} \)
\( 2^{12} \cdot 13^{3} \)
$1.28875$
$(a+1), (2a+3)$
0
$\Z/2\Z$
$\textsf{yes}$
$-4$
$\mathrm{U}(1)$
✓
✓
$13$
13Cs.4.1
$1$
\( 2 \)
$1$
$3.620750525$
1.810375262
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 i + 3\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(2i+3\right){x}$
2704.3-a1
2704.3-a
$1$
$1$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
2704.3
\( 2^{4} \cdot 13^{2} \)
\( 2^{8} \cdot 13^{8} \)
$1.28875$
$(a+1), (2a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cn
$1$
\( 1 \)
$1$
$1.571208998$
1.571208998
\( 512 a + 768 \)
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( -16 i + 3\) , \( 7 i + 18\bigr] \)
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(-16i+3\right){x}+7i+18$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.