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
257.2-a1
257.2-a
$4$
$4$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
257.2
\( 257 \)
\( 257^{2} \)
$0.71557$
$(a-16)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$4.352080368$
0.544010046
\( \frac{270524400}{66049} a - \frac{4278058753}{66049} \)
\( \bigl[i\) , \( i\) , \( 1\) , \( -i + 5\) , \( -3 i - 1\bigr] \)
${y}^2+i{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-i+5\right){x}-3i-1$
257.2-a2
257.2-a
$4$
$4$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
257.2
\( 257 \)
\( 257^{4} \)
$0.71557$
$(a-16)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$2.176040184$
0.544010046
\( \frac{1925135139585}{4362470401} a + \frac{1721475236576}{4362470401} \)
\( \bigl[i\) , \( i\) , \( 1\) , \( 4 i + 5\) , \( -4 i - 12\bigr] \)
${y}^2+i{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(4i+5\right){x}-4i-12$
257.2-a3
257.2-a
$4$
$4$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
257.2
\( 257 \)
\( 257 \)
$0.71557$
$(a-16)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$8.704160737$
0.544010046
\( -\frac{123616}{257} a + \frac{115409}{257} \)
\( \bigl[1\) , \( -i\) , \( i\) , \( -i\) , \( 0\bigr] \)
${y}^2+{x}{y}+i{y}={x}^{3}-i{x}^{2}-i{x}$
257.2-a4
257.2-a
$4$
$4$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
257.2
\( 257 \)
\( 257 \)
$0.71557$
$(a-16)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$2.176040184$
0.544010046
\( -\frac{137925296129}{257} a + \frac{1098686595824}{257} \)
\( \bigl[i\) , \( i\) , \( 1\) , \( -6 i + 85\) , \( -274 i - 34\bigr] \)
${y}^2+i{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-6i+85\right){x}-274i-34$
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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.