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-a3 11.1-a $3$
$25$
\(\Q(\sqrt{-33}) \) $2$
$[0, 1]$
11.1
\( 11 \)
\( 3^{12} \cdot 11^{2} \)
$1.86971$
$(11,a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$5$
5Cs.4.1 $1$
\( 2 \)
$0.882972080$
$9.257718117$
5.691856546
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( -3\) , \( -5\bigr] \) ${y}^2+{y}={x}^3-3{x}-5$
11.1-b3 11.1-b $3$
$25$
\(\Q(\sqrt{-33}) \) $2$
$[0, 1]$
11.1
\( 11 \)
\( 3^{12} \cdot 11^{2} \)
$1.86971$
$(11,a)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$5$
5Cs.4.1 $1$
\( 2 \)
$1$
$9.257718117$
3.223123738
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( 0\) , \( a\) , \( -3\) , \( 13\bigr] \) ${y}^2+a{y}={x}^3-3{x}+13$
11.1-c3 11.1-c $3$
$25$
\(\Q(\sqrt{-33}) \) $2$
$[0, 1]$
11.1
\( 11 \)
\( 11^{2} \)
$1.86971$
$(11,a)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$5$
5Cs.1.1 $1$
\( 2 \)
$1$
$9.257718117$
0.128924949
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3-{x}^2$
11.1-d3 11.1-d $3$
$25$
\(\Q(\sqrt{-33}) \) $2$
$[0, 1]$
11.1
\( 11 \)
\( 11^{2} \)
$1.86971$
$(11,a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$5$
5Cs.4.1 $1$
\( 2 \)
$0.306230066$
$9.257718117$
1.974034794
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( 1\) , \( a\) , \( 0\) , \( 8\bigr] \) ${y}^2+a{y}={x}^3+{x}^2+8$
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Magma
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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.
