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 $3$
$25$
\(\Q(\zeta_{11})^+\) $5$
$[5, 0]$
11.1
\( 11 \)
\( - 11^{5} \)
$13.74242$
$(a^2+a-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$5$
5B.1.2 $15625$
\( 5 \)
$1$
$0.001053940$
0.680488632
\( -\frac{52893159101157376}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$
11.1-a2 11.1-a $3$
$25$
\(\Q(\zeta_{11})^+\) $5$
$[5, 0]$
11.1
\( 11 \)
\( - 11^{25} \)
$13.74242$
$(a^2+a-2)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$5$
5Cs.1.1 $25$
\( 5^{2} \)
$1$
$3.293564976$
0.680488632
\( -\frac{122023936}{161051} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$
11.1-a3 11.1-a $3$
$25$
\(\Q(\zeta_{11})^+\) $5$
$[5, 0]$
11.1
\( 11 \)
\( - 11^{5} \)
$13.74242$
$(a^2+a-2)$
0
$\Z/25\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$5$
5B.1.1 $1$
\( 5 \)
$1$
$10292.39055$
0.680488632
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}$
Download
displayed columns for
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.
