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-a2
8.1-a
$4$
$4$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
8.1
\( 2^{3} \)
\( 2^{22} \)
$1.16409$
$(2,a+1)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$2.176177662$
$21.87465325$
1.536384471
\( -128955875202 a + 499443959016 \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -208 a - 806\) , \( -1388 a - 5366\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(-208a-806\right){x}-1388a-5366$
8.1-b2
8.1-b
$4$
$4$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
8.1
\( 2^{3} \)
\( 2^{10} \)
$1.16409$
$(2,a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2 \)
$1$
$5.468663313$
1.412002795
\( -128955875202 a + 499443959016 \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -3235 a - 12521\) , \( 67026 a + 259595\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3235a-12521\right){x}+67026a+259595$
8.1-c2
8.1-c
$4$
$4$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
8.1
\( 2^{3} \)
\( 2^{22} \)
$1.16409$
$(2,a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$2.176177662$
$5.468663313$
1.536384471
\( -128955875202 a + 499443959016 \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( -208 a - 806\) , \( 1388 a + 5366\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(-208a-806\right){x}+1388a+5366$
8.1-d2
8.1-d
$4$
$4$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
8.1
\( 2^{3} \)
\( 2^{10} \)
$1.16409$
$(2,a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2 \)
$1$
$21.87465325$
1.412002795
\( -128955875202 a + 499443959016 \)
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 10 a - 49\) , \( -36 a + 125\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(10a-49\right){x}-36a+125$
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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.