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
2888.1-a1
2888.1-a
$1$
$1$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
2888.1
\( 2^{3} \cdot 19^{2} \)
\( 2^{4} \cdot 19^{2} \)
$1.31014$
$(a+1), (19)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$1$
\( 2 \)
$0.065414869$
$6.794444758$
1.777830871
\( -\frac{1024}{19} \)
\( \bigl[0\) , \( i\) , \( i + 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+\left(i+1\right){y}={x}^{3}+i{x}^{2}$
2888.1-b1
2888.1-b
$1$
$1$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
2888.1
\( 2^{3} \cdot 19^{2} \)
\( 2^{10} \cdot 19^{2} \)
$1.31014$
$(a+1), (19)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$1$
\( 2 \)
$0.103366441$
$4.606662983$
1.904697431
\( -\frac{31250}{19} \)
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 2\) , \( -2 i\bigr] \)
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+2{x}-2i$
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.