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
8.1-a3
8.1-a
$4$
$4$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
8.1
\( 2^{3} \)
\( 2^{20} \)
$1.16409$
$(2,a+1)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1.088088831$
$21.87465325$
1.536384471
\( 1000188 \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -168 a - 646\) , \( -2548 a - 9870\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(-168a-646\right){x}-2548a-9870$
8.1-b3
8.1-b
$4$
$4$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
8.1
\( 2^{3} \)
\( 2^{8} \)
$1.16409$
$(2,a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$4$
\( 2 \)
$1$
$21.87465325$
1.412002795
\( 1000188 \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -2605 a - 10081\) , \( 141300 a + 547257\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2605a-10081\right){x}+141300a+547257$
8.1-c3
8.1-c
$4$
$4$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
8.1
\( 2^{3} \)
\( 2^{20} \)
$1.16409$
$(2,a+1)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1.088088831$
$21.87465325$
1.536384471
\( 1000188 \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( -168 a - 646\) , \( 2548 a + 9870\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(-168a-646\right){x}+2548a+9870$
8.1-d3
8.1-d
$4$
$4$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
8.1
\( 2^{3} \)
\( 2^{8} \)
$1.16409$
$(2,a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$4$
\( 2 \)
$1$
$21.87465325$
1.412002795
\( 1000188 \)
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -9\) , \( -2 a - 7\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}-9{x}-2a-7$
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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.