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-a5
8.2-a
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
8.2
\( 2^{3} \)
\( 2^{10} \)
$6.10679$
$(-a)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$365.5377388$
0.867070267
\( 2973144 a^{3} - 5002655 a^{2} - 8485568 a + 8881408 \)
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( 3 a^{3} - 2 a^{2} - 9 a - 6\) , \( 6 a^{3} - 3 a^{2} - 22 a - 13\bigr] \)
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a^{3}-2a^{2}-9a-6\right){x}+6a^{3}-3a^{2}-22a-13$
16.2-a1
16.2-a
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
16.2
\( 2^{4} \)
\( 2^{10} \)
$6.65950$
$(-a)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$928.5469574$
1.101275426
\( 2973144 a^{3} - 5002655 a^{2} - 8485568 a + 8881408 \)
\( \bigl[a^{3} - 4 a\) , \( -a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( -6 a^{3} + 12 a^{2} + 12 a - 24\) , \( 9 a^{3} - 10 a^{2} - 32 a + 7\bigr] \)
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a^{3}+12a^{2}+12a-24\right){x}+9a^{3}-10a^{2}-32a+7$
64.3-b4
64.3-b
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
64.3
\( 2^{6} \)
\( 2^{16} \)
$7.91952$
$(-a)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$262.6438976$
1.246003847
\( 2973144 a^{3} - 5002655 a^{2} - 8485568 a + 8881408 \)
\( \bigl[a^{2} - 2\) , \( a^{2} - 2 a - 2\) , \( 0\) , \( 3 a^{3} - 5 a^{2} - 6 a - 1\) , \( 2 a^{3} - 15 a^{2} + 14 a + 17\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(3a^{3}-5a^{2}-6a-1\right){x}+2a^{3}-15a^{2}+14a+17$
64.3-c6
64.3-c
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
64.3
\( 2^{6} \)
\( 2^{16} \)
$7.91952$
$(-a)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{2} \)
$0.045953750$
$2287.551090$
1.994820489
\( 2973144 a^{3} - 5002655 a^{2} - 8485568 a + 8881408 \)
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( -3 a^{3} + 5 a^{2} + 6 a - 14\) , \( 2 a^{3} - 6 a^{2} - 5 a + 13\bigr] \)
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-1\right){x}^{2}+\left(-3a^{3}+5a^{2}+6a-14\right){x}+2a^{3}-6a^{2}-5a+13$
968.2-b5
968.2-b
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
968.2
\( 2^{3} \cdot 11^{2} \)
\( 2^{10} \cdot 11^{6} \)
$11.12144$
$(-a), (-a^3+2a^2+2a-1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$203.6877551$
1.932622299
\( 2973144 a^{3} - 5002655 a^{2} - 8485568 a + 8881408 \)
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{3} - 4 a - 2\) , \( a^{3} - 3 a\) , \( 30 a^{3} + a^{2} - 132 a - 98\) , \( -265 a^{3} + 57 a^{2} + 1077 a + 585\bigr] \)
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{3}-4a-2\right){x}^{2}+\left(30a^{3}+a^{2}-132a-98\right){x}-265a^{3}+57a^{2}+1077a+585$
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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.