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-A4 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
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2 \)
$1$
$10.09699607$
0.526342305
\( -\frac{174588745152190}{2783} a^{2} - \frac{130042620481635}{2783} a + \frac{1327777229138}{2783} \)
\( \bigl[a^{2} + a\) , \( -a\) , \( a^{2} + 1\) , \( 174 a^{2} - 85 a - 169\) , \( 1133 a^{2} - 241 a - 824\bigr] \) ${y}^2+\left(a^{2}+a\right){x}{y}+\left(a^{2}+1\right){y}={x}^{3}-a{x}^{2}+\left(174a^{2}-85a-169\right){x}+1133a^{2}-241a-824$
5819.3-A3 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
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2B $4$
\( 2^{2} \)
$1$
$0.903615520$
1.507334885
\( -\frac{174588745152190}{2783} a^{2} - \frac{130042620481635}{2783} a + \frac{1327777229138}{2783} \)
\( \bigl[a^{2} + 1\) , \( -a^{2} + a\) , \( a^{2} + 1\) , \( -743 a^{2} - 559 a - 91\) , \( 16358 a^{2} + 3009 a - 7365\bigr] \) ${y}^2+\left(a^{2}+1\right){x}{y}+\left(a^{2}+1\right){y}={x}^{3}+\left(-a^{2}+a\right){x}^{2}+\left(-743a^{2}-559a-91\right){x}+16358a^{2}+3009a-7365$
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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.
