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
8.2-a3
8.2-a
$6$
$8$
4.4.11348.1
$4$
$[4, 0]$
8.2
\( 2^{3} \)
\( - 2^{4} \)
$12.34481$
$(-a-1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$751.8733911$
0.882256902
\( 1068917 a^{3} - 1698543 a^{2} - 4344039 a + 3628683 \)
\( \bigl[a + 1\) , \( a^{3} - 5 a - 4\) , \( a^{3} - a^{2} - 4 a\) , \( -6 a^{3} + 4 a^{2} + 28 a + 14\) , \( 19 a^{3} - 5 a^{2} - 98 a - 53\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-5a-4\right){x}^{2}+\left(-6a^{3}+4a^{2}+28a+14\right){x}+19a^{3}-5a^{2}-98a-53$
8.2-b1
8.2-b
$6$
$8$
4.4.11348.1
$4$
$[4, 0]$
8.2
\( 2^{3} \)
\( - 2^{4} \)
$12.34481$
$(-a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.172750202$
$915.7167659$
2.969956322
\( 1068917 a^{3} - 1698543 a^{2} - 4344039 a + 3628683 \)
\( \bigl[a^{3} - 4 a - 3\) , \( a^{2} - 4\) , \( a + 1\) , \( -11 a^{3} + 30 a^{2} + 6 a - 5\) , \( 7 a^{3} - 17 a^{2} + 2 a + 7\bigr] \)
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-11a^{3}+30a^{2}+6a-5\right){x}+7a^{3}-17a^{2}+2a+7$
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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.