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
59.3-a1
59.3-a
$1$
$1$
\(\Q(\zeta_{20})^+\)
$4$
$[4, 0]$
59.3
\( 59 \)
\( - 59^{3} \)
$6.65289$
$(a^3+a^2-4a-1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Nn
$1$
\( 1 \)
$1$
$67.12316258$
1.500919544
\( \frac{3559234608}{205379} a^{3} - \frac{7434481239}{205379} a^{2} - \frac{3401019009}{205379} a + \frac{8873009136}{205379} \)
\( \bigl[a^{3} + a^{2} - 2 a - 3\) , \( a + 1\) , \( 1\) , \( 2 a^{2} + 3 a - 1\) , \( -2 a^{3} - 3 a^{2} + 4 a + 4\bigr] \)
${y}^2+\left(a^{3}+a^{2}-2a-3\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a^{2}+3a-1\right){x}-2a^{3}-3a^{2}+4a+4$
59.3-b1
59.3-b
$1$
$1$
\(\Q(\zeta_{20})^+\)
$4$
$[4, 0]$
59.3
\( 59 \)
\( - 59^{3} \)
$6.65289$
$(a^3+a^2-4a-1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Nn
$1$
\( 3 \)
$0.003152340$
$1465.929300$
1.239973629
\( \frac{3559234608}{205379} a^{3} - \frac{7434481239}{205379} a^{2} - \frac{3401019009}{205379} a + \frac{8873009136}{205379} \)
\( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{3} + a^{2} - 2 a - 3\) , \( -2 a^{3} - a^{2} + 6 a + 3\) , \( 3 a^{3} + 4 a^{2} - 5 a - 5\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-2a-3\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-2a^{3}-a^{2}+6a+3\right){x}+3a^{3}+4a^{2}-5a-5$
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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.