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
253.1-A1
253.1-A
$6$
$8$
3.1.23.1
$3$
$[1, 1]$
253.1
\( 11 \cdot 23 \)
\( - 11^{2} \cdot 23 \)
$1.07776$
$(a^2+a-2), (-a^2-2a+2)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$40.38798431$
0.526342305
\( \frac{417863}{2783} a^{2} - \frac{34767}{2783} a + \frac{3149985}{2783} \)
\( \bigl[a^{2} + a + 1\) , \( -a^{2} - a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
${y}^2+\left(a^{2}+a+1\right){x}{y}={x}^{3}+\left(-a^{2}-a-1\right){x}^{2}+{x}$
5819.3-A1
5819.3-A
$6$
$8$
3.1.23.1
$3$
$[1, 1]$
5819.3
\( 11 \cdot 23^{2} \)
\( - 11^{2} \cdot 23^{7} \)
$1.81751$
$(a^2+a-2), (-a^2-2a+2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$7.228924160$
1.507334885
\( \frac{417863}{2783} a^{2} - \frac{34767}{2783} a + \frac{3149985}{2783} \)
\( \bigl[a^{2}\) , \( -a^{2} + a\) , \( 1\) , \( 3 a^{2} - a + 2\) , \( -3 a^{2} + 2 a - 1\bigr] \)
${y}^2+a^{2}{x}{y}+{y}={x}^{3}+\left(-a^{2}+a\right){x}^{2}+\left(3a^{2}-a+2\right){x}-3a^{2}+2a-1$
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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.