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-b1
121.1-b
$2$
$11$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
121.1
\( 11^{2} \)
\( - 11^{3} \)
$17.46636$
$(a^2+a-2)$
$1$
$\Z/11\Z$
$\textsf{potential}$
$-11$
$N(\mathrm{U}(1))$
✓
✓
✓
$11$
11B.1.1[5]
$1$
\( 2 \)
$0.089785156$
$28099.20145$
1.72316863
\( -32768 \)
\( \bigl[0\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 1\) , \( a^{3} + a^{2} - 2 a - 2\) , \( 9 a^{4} - 16 a^{3} - 23 a^{2} + 45 a - 10\) , \( -38 a^{4} + 67 a^{3} + 96 a^{2} - 188 a + 43\bigr] \)
${y}^2+\left(a^{3}+a^{2}-2a-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+3a+1\right){x}^{2}+\left(9a^{4}-16a^{3}-23a^{2}+45a-10\right){x}-38a^{4}+67a^{3}+96a^{2}-188a+43$
121.1-b2
121.1-b
$2$
$11$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
121.1
\( 11^{2} \)
\( - 11^{9} \)
$17.46636$
$(a^2+a-2)$
$1$
$\mathsf{trivial}$
$\textsf{potential}$
$-11$
$N(\mathrm{U}(1))$
✓
✓
✓
$11$
11B.1.10[5]
$1$
\( 2 \)
$0.987636717$
$21.11134594$
1.72316863
\( -32768 \)
\( \bigl[0\) , \( -a^{4} + 4 a^{2} + a - 2\) , \( a^{4} - 4 a^{2} + 3\) , \( -4 a^{4} + 9 a^{3} - a^{2} - 3 a\) , \( -13 a^{4} + 34 a^{3} - 6 a^{2} - 25 a + 5\bigr] \)
${y}^2+\left(a^{4}-4a^{2}+3\right){y}={x}^{3}+\left(-a^{4}+4a^{2}+a-2\right){x}^{2}+\left(-4a^{4}+9a^{3}-a^{2}-3a\right){x}-13a^{4}+34a^{3}-6a^{2}-25a+5$
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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.