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
121.1-a1
121.1-a
$2$
$11$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
121.1
\( 11^{2} \)
\( - 11^{4} \)
$17.46636$
$(a^2+a-2)$
0
$\Z/11\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$11$
11B.1.1[5]
$1$
\( 1 \)
$1$
$17090.60992$
1.16731165
\( -24729001 \)
\( \bigl[a^{4} - 3 a^{2} + 1\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( a^{2} + a - 1\) , \( -15 a^{4} + 38 a^{3} - 10 a^{2} - 19 a\) , \( 94 a^{4} - 262 a^{3} + 77 a^{2} + 174 a - 46\bigr] \)
${y}^2+\left(a^{4}-3a^{2}+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+2a\right){x}^{2}+\left(-15a^{4}+38a^{3}-10a^{2}-19a\right){x}+94a^{4}-262a^{3}+77a^{2}+174a-46$
121.1-d1
121.1-d
$2$
$11$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
121.1
\( 11^{2} \)
\( - 11^{10} \)
$17.46636$
$(a^2+a-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$11$
11B.1.10[5]
$121$
\( 1 \)
$1$
$1.102971008$
1.10297101
\( -24729001 \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -30\) , \( -76\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-30{x}-76$
Download
displayed columns for
results
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.