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
387.2-a1
387.2-a
$1$
$1$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
387.2
\( 3^{2} \cdot 43 \)
\( 3^{7} \cdot 43 \)
$1.12101$
$(-a-1), (3a-5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{2} \)
$0.019578494$
$5.275237659$
0.584246746
\( \frac{4096}{129} a + \frac{241664}{129} \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( a + 1\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}+\left(a+1\right){x}$
387.2-b1
387.2-b
$3$
$9$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
387.2
\( 3^{2} \cdot 43 \)
\( 3^{15} \cdot 43 \)
$1.12101$
$(-a-1), (3a-5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.2
$1$
\( 2^{2} \)
$0.115788454$
$2.345414412$
1.536242707
\( -\frac{3128360960}{846369} a - \frac{4018143232}{846369} \)
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 4 a - 11\) , \( 10 a - 7\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-11\right){x}+10a-7$
387.2-b2
387.2-b
$3$
$9$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
387.2
\( 3^{2} \cdot 43 \)
\( 3^{9} \cdot 43^{3} \)
$1.12101$
$(-a-1), (3a-5)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3Cs.1.1
$1$
\( 2^{2} \cdot 3 \)
$0.347365362$
$2.345414412$
1.536242707
\( \frac{340295680}{2146689} a + \frac{3946938368}{2146689} \)
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( -9\) , \( a\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}-9{x}+a$
387.2-b3
387.2-b
$3$
$9$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
387.2
\( 3^{2} \cdot 43 \)
\( 3^{7} \cdot 43 \)
$1.12101$
$(-a-1), (3a-5)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B.1.1
$1$
\( 2^{2} \)
$1.042096086$
$2.345414412$
1.536242707
\( -\frac{2235072512}{129} a + \frac{2686877696}{129} \)
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 20 a + 35\) , \( -63 a + 97\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(20a+35\right){x}-63a+97$
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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.