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
121.3-a1
121.3-a
$2$
$2$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
121.3
\( 11^{2} \)
\( - 11^{9} \)
$1.02666$
$(2a+1)$
0
$\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2 \)
$1$
$6.438947969$
0.929382085
\( 1728 \)
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -16 a + 26\) , \( 13 a - 24\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-16a+26\right){x}+13a-24$
121.3-a2
121.3-a
$2$
$2$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
121.3
\( 11^{2} \)
\( - 11^{9} \)
$1.02666$
$(2a+1)$
0
$\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2 \)
$1$
$6.438947969$
0.929382085
\( 1728 \)
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 209 a - 361\) , \( -181 a + 314\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(209a-361\right){x}-181a+314$
121.3-b1
121.3-b
$2$
$3$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
121.3
\( 11^{2} \)
\( 11^{2} \)
$1.02666$
$(2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 1 \)
$0.194855274$
$10.87456613$
1.223385920
\( 0 \)
\( \bigl[0\) , \( -a\) , \( a\) , \( 1\) , \( -1\bigr] \)
${y}^2+a{y}={x}^{3}-a{x}^{2}+{x}-1$
121.3-b2
121.3-b
$2$
$3$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
121.3
\( 11^{2} \)
\( 11^{2} \)
$1.02666$
$(2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 1 \)
$0.064951758$
$32.62369841$
1.223385920
\( 0 \)
\( \bigl[0\) , \( a\) , \( 1\) , \( 1\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}+a{x}^{2}+{x}$
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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.