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
16.2-a1
16.2-a
$2$
$2$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
16.2
\( 2^{4} \)
\( - 2^{11} \)
$1.02666$
$(-a-2), (-a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$13.74710193$
1.196531640
\( -\frac{18649}{2} a + 33120 \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 31 a + 72\) , \( 26 a + 60\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(31a+72\right){x}+26a+60$
16.2-a2
16.2-a
$2$
$2$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
16.2
\( 2^{4} \)
\( - 2^{13} \)
$1.02666$
$(-a-2), (-a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$13.74710193$
1.196531640
\( \frac{1241}{4} a + 736 \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( a\) , \( 130 a - 436\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+a{x}+130a-436$
16.2-b1
16.2-b
$2$
$2$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
16.2
\( 2^{4} \)
\( - 2^{11} \)
$1.02666$
$(-a-2), (-a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$24.99543515$
2.175573380
\( -\frac{18649}{2} a + 33120 \)
\( \bigl[a\) , \( -a\) , \( a\) , \( 4 a - 19\) , \( -5 a + 14\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(4a-19\right){x}-5a+14$
16.2-b2
16.2-b
$2$
$2$
\(\Q(\sqrt{33}) \)
$2$
$[2, 0]$
16.2
\( 2^{4} \)
\( - 2^{13} \)
$1.02666$
$(-a-2), (-a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$24.99543515$
2.175573380
\( \frac{1241}{4} a + 736 \)
\( \bigl[a\) , \( 1\) , \( a\) , \( -3 a - 8\) , \( -3 a - 8\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-3a-8\right){x}-3a-8$
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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.