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-a2
8.2-a
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
8.2
\( 2^{3} \)
\( - 2^{11} \)
$6.10679$
$(-a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$182.7688694$
0.867070267
\( -601 a^{3} + 1330 a^{2} + 1931 a - 2180 \)
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 4 a\) , \( a^{3} - a^{2} - 2 a + 2\) , \( -a^{3} - a^{2} + 4 a + 5\) , \( -a^{3} - a^{2} + 4 a + 1\bigr] \)
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a\right){x}^{2}+\left(-a^{3}-a^{2}+4a+5\right){x}-a^{3}-a^{2}+4a+1$
16.2-a3
16.2-a
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
16.2
\( 2^{4} \)
\( - 2^{11} \)
$6.65950$
$(-a)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$928.5469574$
1.101275426
\( -601 a^{3} + 1330 a^{2} + 1931 a - 2180 \)
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 3 a + 2\) , \( a^{3} - 3 a\) , \( -2 a^{3} + 6 a + 2\) , \( -a^{3} + 3 a + 1\bigr] \)
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{3}+3a+2\right){x}^{2}+\left(-2a^{3}+6a+2\right){x}-a^{3}+3a+1$
64.3-b3
64.3-b
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
64.3
\( 2^{6} \)
\( - 2^{17} \)
$7.91952$
$(-a)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$262.6438976$
1.246003847
\( -601 a^{3} + 1330 a^{2} + 1931 a - 2180 \)
\( \bigl[a^{2} - a - 2\) , \( -a^{2} + 3\) , \( a^{3} - a^{2} - 2 a + 2\) , \( -2 a^{3} + 2 a^{2} + 6 a - 1\) , \( -5 a^{3} + 7 a^{2} + 14 a - 12\bigr] \)
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-2a^{3}+2a^{2}+6a-1\right){x}-5a^{3}+7a^{2}+14a-12$
64.3-c4
64.3-c
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
64.3
\( 2^{6} \)
\( - 2^{17} \)
$7.91952$
$(-a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$0.022976875$
$1143.775545$
1.994820489
\( -601 a^{3} + 1330 a^{2} + 1931 a - 2180 \)
\( \bigl[a\) , \( -a^{2} + 2\) , \( a\) , \( -a^{2} + 1\) , \( 0\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-a^{2}+1\right){x}$
968.2-b2
968.2-b
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
968.2
\( 2^{3} \cdot 11^{2} \)
\( - 2^{11} \cdot 11^{6} \)
$11.12144$
$(-a), (-a^3+2a^2+2a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$203.6877551$
1.932622299
\( -601 a^{3} + 1330 a^{2} + 1931 a - 2180 \)
\( \bigl[a^{3} - 4 a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -6 a^{3} + 9 a^{2} + 18 a - 15\) , \( -8 a^{3} + 13 a^{2} + 23 a - 22\bigr] \)
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-6a^{3}+9a^{2}+18a-15\right){x}-8a^{3}+13a^{2}+23a-22$
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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.