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-a5
33.1-a
$6$
$8$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
33.1
\( 3 \cdot 11 \)
\( 3^{6} \cdot 11^{8} \)
$1.23034$
$(-2a+7), (-4a-9)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$0.739425251$
$8.936252827$
2.300502718
\( \frac{347873904937}{395307} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( -146\) , \( 621\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}-146{x}+621$
33.1-b5
33.1-b
$6$
$8$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
33.1
\( 3 \cdot 11 \)
\( 3^{6} \cdot 11^{8} \)
$1.23034$
$(-2a+7), (-4a-9)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$1.883253066$
0.327832279
\( \frac{347873904937}{395307} \)
\( \bigl[1\) , \( -a\) , \( a\) , \( -53920 a - 127910\) , \( -11482951 a - 27240791\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-53920a-127910\right){x}-11482951a-27240791$
363.1-c5
363.1-c
$6$
$8$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
363.1
\( 3 \cdot 11^{2} \)
\( 3^{6} \cdot 11^{14} \)
$2.24064$
$(-2a+7), (-4a-9)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \cdot 3 \)
$1$
$1.236903227$
1.291903287
\( \frac{347873904937}{395307} \)
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 12895 a - 43514\) , \( -1355151 a + 4569820\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(12895a-43514\right){x}-1355151a+4569820$
363.1-d5
363.1-d
$6$
$8$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
363.1
\( 3 \cdot 11^{2} \)
\( 3^{6} \cdot 11^{14} \)
$2.24064$
$(-2a+7), (-4a-9)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \cdot 3 \)
$1$
$1.236903227$
1.291903287
\( \frac{347873904937}{395307} \)
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -12893 a - 30620\) , \( 1368045 a + 3245289\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-12893a-30620\right){x}+1368045a+3245289$
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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.