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
275.1-a1
275.1-a
$4$
$4$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
275.1
\( 5^{2} \cdot 11 \)
\( 5^{2} \cdot 11^{2} \)
$2.09040$
$(-4a-9), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2 \)
$1.506787596$
$16.93058676$
4.440859943
\( \frac{59319}{55} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+{x}$
275.1-b1
275.1-b
$4$
$4$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
275.1
\( 5^{2} \cdot 11 \)
\( 5^{2} \cdot 11^{2} \)
$2.09040$
$(-4a-9), (5)$
$2$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2 \)
$1.858870826$
$11.85112914$
1.917440855
\( \frac{59319}{55} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 299 a + 709\) , \( -3776 a - 8958\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(299a+709\right){x}-3776a-8958$
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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.