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
25.2-a1
25.2-a
$2$
$11$
\(\Q(\sqrt{11}) \)
$2$
$[2, 0]$
25.2
\( 5^{2} \)
\( 5^{6} \)
$1.32541$
$(a-4)$
0
$\mathsf{trivial}$
$\textsf{potential}$
$-11$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 1 \)
$1$
$10.31419920$
1.554924035
\( -32768 \)
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 6 a - 14\) , \( -9 a + 27\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a-14\right){x}-9a+27$
25.2-a2
25.2-a
$2$
$11$
\(\Q(\sqrt{11}) \)
$2$
$[2, 0]$
25.2
\( 5^{2} \)
\( 5^{6} \)
$1.32541$
$(a-4)$
0
$\mathsf{trivial}$
$\textsf{potential}$
$-11$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 1 \)
$1$
$10.31419920$
1.554924035
\( -32768 \)
\( \bigl[0\) , \( a + 1\) , \( a\) , \( 6 a - 14\) , \( 9 a - 30\bigr] \)
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-14\right){x}+9a-30$
25.2-b1
25.2-b
$2$
$2$
\(\Q(\sqrt{11}) \)
$2$
$[2, 0]$
25.2
\( 5^{2} \)
\( 5^{9} \)
$1.32541$
$(a-4)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2 \)
$1.282876014$
$8.224640586$
1.590652365
\( 1728 \)
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 2 a + 9\) , \( 4 a + 7\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(2a+9\right){x}+4a+7$
25.2-b2
25.2-b
$2$
$2$
\(\Q(\sqrt{11}) \)
$2$
$[2, 0]$
25.2
\( 5^{2} \)
\( 5^{9} \)
$1.32541$
$(a-4)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2 \)
$0.641438007$
$16.44928117$
1.590652365
\( 1728 \)
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -93 a - 306\) , \( -251 a - 833\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-93a-306\right){x}-251a-833$
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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.