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
11.1-a1 11.1-a $3$
$25$
\(\Q(\sqrt{-11}) \) $2$
$[0, 1]$
11.1
\( 11 \)
\( 11^{2} \)
$0.53974$
$(-2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2, 5$
2Cn , 5B.1.2 $1$
\( 2 \)
$1$
$0.370308724$
0.446609125
\( -\frac{52893159101157376}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$
11.1-a2 11.1-a $3$
$25$
\(\Q(\sqrt{-11}) \) $2$
$[0, 1]$
11.1
\( 11 \)
\( 11^{10} \)
$0.53974$
$(-2a+1)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2, 5$
2Cn , 5Cs.1.1 $1$
\( 2 \cdot 5 \)
$1$
$1.851543623$
0.446609125
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$
11.1-a3 11.1-a $3$
$25$
\(\Q(\sqrt{-11}) \) $2$
$[0, 1]$
11.1
\( 11 \)
\( 11^{2} \)
$0.53974$
$(-2a+1)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2, 5$
2Cn , 5B.1.1 $1$
\( 2 \)
$1$
$9.257718117$
0.446609125
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}$
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Pari/GP
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Magma
Oscar
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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.
