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-a8
8.2-a
$8$
$16$
3.3.316.1
$3$
$[3, 0]$
8.2
\( 2^{3} \)
\( - 2^{11} \)
$2.24645$
$(a)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$172.6937124$
0.607173770
\( 103101005876 a^{2} - 290083733531 a + 113696309796 \)
\( \bigl[a\) , \( -a^{2} + a + 3\) , \( a\) , \( -2419 a^{2} + 1279 a + 10275\) , \( -4236156 a^{2} + 2242268 a + 18000022\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-2419a^{2}+1279a+10275\right){x}-4236156a^{2}+2242268a+18000022$
16.2-a2
16.2-a
$8$
$16$
3.3.316.1
$3$
$[3, 0]$
16.2
\( 2^{4} \)
\( - 2^{11} \)
$2.52156$
$(a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$23.39817653$
1.316250266
\( 103101005876 a^{2} - 290083733531 a + 113696309796 \)
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -6407 a^{2} + 3208 a + 26891\) , \( 17854891 a^{2} - 9448825 a - 75864197\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6407a^{2}+3208a+26891\right){x}+17854891a^{2}-9448825a-75864197$
128.5-e7
128.5-e
$8$
$16$
3.3.316.1
$3$
$[3, 0]$
128.5
\( 2^{7} \)
\( - 2^{23} \)
$3.56602$
$(a), (-a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 2 \)
$1.606078329$
$4.868558216$
2.639215170
\( 103101005876 a^{2} - 290083733531 a + 113696309796 \)
\( \bigl[a^{2} + a - 2\) , \( a + 1\) , \( a^{2} + a - 2\) , \( -188 a^{2} + 103 a + 805\) , \( 92985 a^{2} - 49226 a - 395120\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-188a^{2}+103a+805\right){x}+92985a^{2}-49226a-395120$
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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.