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
5324.6-a2
5324.6-a
$2$
$3$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
5324.6
\( 2^{2} \cdot 11^{3} \)
\( 2^{39} \cdot 11^{9} \)
$2.01952$
$(a), (-a+1), (-2a+3), (2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.2
$1$
\( 2 \)
$2.414156031$
$0.240778672$
1.757617297
\( \frac{4070378798731}{11811160064} a + \frac{106097102447}{5905580032} \)
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 395 a - 48\) , \( 6353 a - 210\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(395a-48\right){x}+6353a-210$
42592.18-c1
42592.18-c
$2$
$3$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
42592.18
\( 2^{5} \cdot 11^{3} \)
\( 2^{51} \cdot 11^{3} \)
$3.39641$
$(a), (-a+1), (-2a+3), (2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2^{2} \)
$1.469814848$
$0.399286256$
3.549097701
\( \frac{4070378798731}{11811160064} a + \frac{106097102447}{5905580032} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -148 a + 49\) , \( -135 a + 1967\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-148a+49\right){x}-135a+1967$
42592.6-d1
42592.6-d
$2$
$3$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
42592.6
\( 2^{5} \cdot 11^{3} \)
\( 2^{51} \cdot 11^{3} \)
$3.39641$
$(a), (-a+1), (-2a+3), (2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2^{3} \cdot 3 \cdot 5 \)
$0.103483218$
$0.399286256$
7.496292234
\( \frac{4070378798731}{11811160064} a + \frac{106097102447}{5905580032} \)
\( \bigl[a\) , \( a\) , \( a\) , \( 148 a - 98\) , \( -1422 a + 1051\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(148a-98\right){x}-1422a+1051$
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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.