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
64.1-a1
64.1-a
$1$
$1$
4.4.2624.1
$4$
$[4, 0]$
64.1
\( 2^{6} \)
\( 2^{22} \)
$7.69827$
$(a^3-2a^2-2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$70.51639173$
1.376601271
\( -7045 a^{3} - 6461 a^{2} + 7181 a + 3088 \)
\( \bigl[a^{2} - a - 1\) , \( a^{2} - a - 1\) , \( 0\) , \( -a^{3} + 4 a^{2} + 4 a - 1\) , \( 6 a^{3} - 11 a^{2} - 14 a + 11\bigr] \)
${y}^2+\left(a^{2}-a-1\right){x}{y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(-a^{3}+4a^{2}+4a-1\right){x}+6a^{3}-11a^{2}-14a+11$
64.1-b1
64.1-b
$1$
$1$
4.4.2624.1
$4$
$[4, 0]$
64.1
\( 2^{6} \)
\( 2^{22} \)
$7.69827$
$(a^3-2a^2-2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$70.51639173$
1.376601271
\( -55056 a^{3} + 130663 a^{2} + 117021 a - 154587 \)
\( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{3} + 3 a^{2} - a - 2\) , \( a^{3} - a^{2} - 3 a\) , \( -2 a^{3} + 6 a^{2} - 4 a - 3\) , \( -a^{3} + 5 a^{2} - 3 a - 2\bigr] \)
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(-a^{3}+3a^{2}-a-2\right){x}^{2}+\left(-2a^{3}+6a^{2}-4a-3\right){x}-a^{3}+5a^{2}-3a-2$
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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.