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
33.1-a4
33.1-a
$6$
$8$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
33.1
\( 3 \cdot 11 \)
\( 3^{6} \cdot 11^{2} \)
$1.23034$
$(-2a+7), (-4a-9)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$2.957701004$
$8.936252827$
2.300502718
\( \frac{30664297}{297} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( -6\) , \( -9\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}-6{x}-9$
33.1-b4
33.1-b
$6$
$8$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
33.1
\( 3 \cdot 11 \)
\( 3^{6} \cdot 11^{2} \)
$1.23034$
$(-2a+7), (-4a-9)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$30.13204906$
0.327832279
\( \frac{30664297}{297} \)
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 2399 a - 8090\) , \( -110030 a + 371048\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2399a-8090\right){x}-110030a+371048$
363.1-c4
363.1-c
$6$
$8$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
363.1
\( 3 \cdot 11^{2} \)
\( 3^{6} \cdot 11^{8} \)
$2.24064$
$(-2a+7), (-4a-9)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \cdot 3 \)
$1$
$4.947612911$
1.291903287
\( \frac{30664297}{297} \)
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 575 a - 1934\) , \( 12369 a - 41710\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(575a-1934\right){x}+12369a-41710$
363.1-d4
363.1-d
$6$
$8$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
363.1
\( 3 \cdot 11^{2} \)
\( 3^{6} \cdot 11^{8} \)
$2.24064$
$(-2a+7), (-4a-9)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \cdot 3 \)
$1$
$4.947612911$
1.291903287
\( \frac{30664297}{297} \)
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -573 a - 1360\) , \( -11795 a - 27981\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-573a-1360\right){x}-11795a-27981$
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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.