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-a6
33.1-a
$6$
$8$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
33.1
\( 3 \cdot 11 \)
\( - 3^{3} \cdot 11 \)
$1.23034$
$(-2a+7), (-4a-9)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 1 \)
$5.915402008$
$4.468126413$
2.300502718
\( \frac{181064514814}{99} a + \frac{429535966213}{99} \)
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -944 a - 2235\) , \( -27553 a - 65366\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-944a-2235\right){x}-27553a-65366$
33.1-b6
33.1-b
$6$
$8$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
33.1
\( 3 \cdot 11 \)
\( - 3^{3} \cdot 11 \)
$1.23034$
$(-2a+7), (-4a-9)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 1 \)
$1$
$30.13204906$
0.327832279
\( \frac{181064514814}{99} a + \frac{429535966213}{99} \)
\( \bigl[1\) , \( -a\) , \( a\) , \( -1\) , \( -10 a + 34\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}-{x}-10a+34$
363.1-c6
363.1-c
$6$
$8$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
363.1
\( 3 \cdot 11^{2} \)
\( - 3^{3} \cdot 11^{7} \)
$2.24064$
$(-2a+7), (-4a-9)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \cdot 3 \)
$1$
$4.947612911$
1.291903287
\( \frac{181064514814}{99} a + \frac{429535966213}{99} \)
\( \bigl[1\) , \( 0\) , \( a\) , \( -226 a - 536\) , \( 3110 a + 7369\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-226a-536\right){x}+3110a+7369$
363.1-d6
363.1-d
$6$
$8$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
363.1
\( 3 \cdot 11^{2} \)
\( - 3^{3} \cdot 11^{7} \)
$2.24064$
$(-2a+7), (-4a-9)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \cdot 3 \)
$1$
$2.473806455$
1.291903287
\( \frac{181064514814}{99} a + \frac{429535966213}{99} \)
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 395 a - 1327\) , \( -123291 a + 415770\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(395a-1327\right){x}-123291a+415770$
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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.