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-a2 121.1-a $2$
$11$
\(\Q(\zeta_{11})^+\) $5$
$[5, 0]$
121.1
\( 11^{2} \)
\( - 11^{8} \)
$17.46636$
$(a^2+a-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$11$
11B.1.10[5] $1$
\( 1 \)
$1$
$141.2447101$
1.16731165
\( -121 \)
\( \bigl[a^{2} - 1\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 3\) , \( 2 a^{4} - 5 a^{3} - 6 a^{2} + 13 a - 1\) , \( 16 a^{4} - 31 a^{3} - 40 a^{2} + 86 a - 22\bigr] \) ${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(2a^{4}-5a^{3}-6a^{2}+13a-1\right){x}+16a^{4}-31a^{3}-40a^{2}+86a-22$
121.1-d2 121.1-d $2$
$11$
\(\Q(\zeta_{11})^+\) $5$
$[5, 0]$
121.1
\( 11^{2} \)
\( - 11^{2} \)
$17.46636$
$(a^2+a-2)$
0
$\Z/11\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$11$
11B.1.1[5] $1$
\( 1 \)
$1$
$16148.59853$
1.10297101
\( -121 \)
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{4} - a^{3} + 5 a^{2} + 4 a - 5\) , \( a^{4} - 3 a^{2}\) , \( -3 a^{4} + 2 a^{3} + 9 a^{2} - 5 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{4}-3a^{2}\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+4a-5\right){x}^{2}+\left(-3a^{4}+2a^{3}+9a^{2}-5a\right){x}+a^{4}-2a^{3}-3a^{2}+6a+1$
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.
