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
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
8.2
\( 2^{3} \)
\( 2^{8} \)
$6.10679$
$(-a)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$365.5377388$
0.867070267
\( -2732527394 a^{3} + 1558959970 a^{2} + 13692770763 a + 7728253510 \)
\( \bigl[a^{2} - 2\) , \( a^{3} - 3 a - 2\) , \( 0\) , \( 9 a^{3} - 25 a^{2} + 14 a + 4\) , \( -30 a^{3} + 72 a^{2} + 25 a - 54\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{3}-3a-2\right){x}^{2}+\left(9a^{3}-25a^{2}+14a+4\right){x}-30a^{3}+72a^{2}+25a-54$
16.2-a6
16.2-a
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
16.2
\( 2^{4} \)
\( 2^{8} \)
$6.65950$
$(-a)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$4$
\( 2 \)
$1$
$116.0683696$
1.101275426
\( -2732527394 a^{3} + 1558959970 a^{2} + 13692770763 a + 7728253510 \)
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + a^{2} + 2 a - 2\) , \( a\) , \( -4 a^{3} + a^{2} + 6 a - 7\) , \( -9 a^{2} - 7 a + 9\bigr] \)
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+a^{2}+2a-2\right){x}^{2}+\left(-4a^{3}+a^{2}+6a-7\right){x}-9a^{2}-7a+9$
64.3-b1
64.3-b
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
64.3
\( 2^{6} \)
\( 2^{14} \)
$7.91952$
$(-a)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$262.6438976$
1.246003847
\( -2732527394 a^{3} + 1558959970 a^{2} + 13692770763 a + 7728253510 \)
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( a^{2} - 2\) , \( 29 a^{3} - 76 a^{2} + 35\) , \( -41 a^{3} + 101 a^{2} + 12 a - 56\bigr] \)
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-1\right){x}^{2}+\left(29a^{3}-76a^{2}+35\right){x}-41a^{3}+101a^{2}+12a-56$
64.3-c2
64.3-c
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
64.3
\( 2^{6} \)
\( 2^{14} \)
$7.91952$
$(-a)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{2} \)
$0.091907500$
$1143.775545$
1.994820489
\( -2732527394 a^{3} + 1558959970 a^{2} + 13692770763 a + 7728253510 \)
\( \bigl[a^{2} - 2\) , \( a^{2} - 1\) , \( a^{2} - a - 2\) , \( -12 a^{3} - 14 a^{2} + 10 a + 4\) , \( 42 a^{3} + 54 a^{2} - 34 a - 32\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-1\right){x}^{2}+\left(-12a^{3}-14a^{2}+10a+4\right){x}+42a^{3}+54a^{2}-34a-32$
968.2-b1
968.2-b
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
968.2
\( 2^{3} \cdot 11^{2} \)
\( 2^{8} \cdot 11^{6} \)
$11.12144$
$(-a), (-a^3+2a^2+2a-1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$101.8438775$
1.932622299
\( -2732527394 a^{3} + 1558959970 a^{2} + 13692770763 a + 7728253510 \)
\( \bigl[a^{3} - 4 a\) , \( a^{3} - 5 a - 2\) , \( a^{2} - 2\) , \( 214 a^{3} - 544 a^{2} - 30 a + 277\) , \( 1464 a^{3} - 3687 a^{2} - 276 a + 1917\bigr] \)
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-5a-2\right){x}^{2}+\left(214a^{3}-544a^{2}-30a+277\right){x}+1464a^{3}-3687a^{2}-276a+1917$
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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.