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-a1
8.2-a
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
8.2
\( 2^{3} \)
\( - 2^{4} \)
$6.10679$
$(-a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$91.38443470$
0.867070267
\( 8986661761218306693 a^{3} + 12242887281724452580 a^{2} - 7024786750071806011 a - 7608271795805318134 \)
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 2 a - 2\) , \( a^{3} - 4 a\) , \( -2 a^{3} - 9 a^{2} - 10 a + 2\) , \( 32 a^{3} + 44 a^{2} - 34 a - 39\bigr] \)
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-2\right){x}^{2}+\left(-2a^{3}-9a^{2}-10a+2\right){x}+32a^{3}+44a^{2}-34a-39$
16.2-a2
16.2-a
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
16.2
\( 2^{4} \)
\( - 2^{4} \)
$6.65950$
$(-a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$16$
\( 1 \)
$1$
$14.50854621$
1.101275426
\( 8986661761218306693 a^{3} + 12242887281724452580 a^{2} - 7024786750071806011 a - 7608271795805318134 \)
\( \bigl[a^{3} - 4 a\) , \( -a^{2} + 1\) , \( a^{2} - a - 2\) , \( -76 a^{3} + 192 a^{2} + 10 a - 99\) , \( 264 a^{3} - 660 a^{2} - 64 a + 352\bigr] \)
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{2}+1\right){x}^{2}+\left(-76a^{3}+192a^{2}+10a-99\right){x}+264a^{3}-660a^{2}-64a+352$
64.3-b6
64.3-b
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
64.3
\( 2^{6} \)
\( - 2^{10} \)
$7.91952$
$(-a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 2 \)
$1$
$32.83048720$
1.246003847
\( 8986661761218306693 a^{3} + 12242887281724452580 a^{2} - 7024786750071806011 a - 7608271795805318134 \)
\( \bigl[a^{3} - 4 a\) , \( -a^{2} + 2\) , \( a^{3} - a^{2} - 2 a + 2\) , \( -33 a^{3} - 40 a^{2} + 22 a + 24\) , \( -293 a^{3} - 393 a^{2} + 229 a + 245\bigr] \)
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-33a^{3}-40a^{2}+22a+24\right){x}-293a^{3}-393a^{2}+229a+245$
64.3-c3
64.3-c
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
64.3
\( 2^{6} \)
\( - 2^{10} \)
$7.91952$
$(-a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.183815000$
$285.9438863$
1.994820489
\( 8986661761218306693 a^{3} + 12242887281724452580 a^{2} - 7024786750071806011 a - 7608271795805318134 \)
\( \bigl[a\) , \( 0\) , \( a^{3} - 4 a\) , \( 8 a^{3} - 32 a^{2} - 39 a + 45\) , \( 76 a^{3} - 57 a^{2} - 167 a + 137\bigr] \)
${y}^2+a{x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(8a^{3}-32a^{2}-39a+45\right){x}+76a^{3}-57a^{2}-167a+137$
968.2-b6
968.2-b
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
968.2
\( 2^{3} \cdot 11^{2} \)
\( - 2^{4} \cdot 11^{6} \)
$11.12144$
$(-a), (-a^3+2a^2+2a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 2^{3} \)
$1$
$12.73048469$
1.932622299
\( 8986661761218306693 a^{3} + 12242887281724452580 a^{2} - 7024786750071806011 a - 7608271795805318134 \)
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a\) , \( a^{3} - 4 a\) , \( -23 a^{3} + 3 a^{2} - 3 a - 9\) , \( -130 a^{3} - 194 a^{2} + 136 a + 140\bigr] \)
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}-a{x}^{2}+\left(-23a^{3}+3a^{2}-3a-9\right){x}-130a^{3}-194a^{2}+136a+140$
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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.