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
59.2-a1
59.2-a
$1$
$1$
4.4.6125.1
$4$
$[4, 0]$
59.2
\( 59 \)
\( - 59^{3} \)
$11.64255$
$(3a^3+4a^2-18a-17)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$175.2162663$
2.238831327
\( \frac{528977945391}{205379} a^{3} + \frac{623147922314}{205379} a^{2} - \frac{3406714985428}{205379} a - \frac{2669026432747}{205379} \)
\( \bigl[a^{3} + a^{2} - 5 a - 3\) , \( -a^{3} - 2 a^{2} + 6 a + 8\) , \( 2 a^{3} + 3 a^{2} - 12 a - 12\) , \( -19 a^{3} + 25 a^{2} + 142 a - 229\) , \( -404 a^{3} + 705 a^{2} + 3109 a - 5954\bigr] \)
${y}^2+\left(a^{3}+a^{2}-5a-3\right){x}{y}+\left(2a^{3}+3a^{2}-12a-12\right){y}={x}^{3}+\left(-a^{3}-2a^{2}+6a+8\right){x}^{2}+\left(-19a^{3}+25a^{2}+142a-229\right){x}-404a^{3}+705a^{2}+3109a-5954$
59.2-b1
59.2-b
$1$
$1$
4.4.6125.1
$4$
$[4, 0]$
59.2
\( 59 \)
\( - 59^{3} \)
$11.64255$
$(3a^3+4a^2-18a-17)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 3 \)
$0.062194364$
$271.9299651$
2.593201710
\( \frac{528977945391}{205379} a^{3} + \frac{623147922314}{205379} a^{2} - \frac{3406714985428}{205379} a - \frac{2669026432747}{205379} \)
\( \bigl[a^{3} + 2 a^{2} - 5 a - 8\) , \( a^{2} + a - 3\) , \( a^{3} + 2 a^{2} - 5 a - 8\) , \( 8 a^{3} + 12 a^{2} - 45 a - 44\) , \( 15 a^{3} + 20 a^{2} - 88 a - 73\bigr] \)
${y}^2+\left(a^{3}+2a^{2}-5a-8\right){x}{y}+\left(a^{3}+2a^{2}-5a-8\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(8a^{3}+12a^{2}-45a-44\right){x}+15a^{3}+20a^{2}-88a-73$
59.2-c1
59.2-c
$1$
$1$
4.4.6125.1
$4$
$[4, 0]$
59.2
\( 59 \)
\( - 59^{3} \)
$11.64255$
$(3a^3+4a^2-18a-17)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 3 \)
$0.065073306$
$330.0357331$
3.293002336
\( -\frac{8193056918637954}{205379} a^{3} + \frac{14306032866590959}{205379} a^{2} + \frac{63063543446609149}{205379} a - \frac{120790269614565170}{205379} \)
\( \bigl[a^{3} + a^{2} - 5 a - 3\) , \( a^{3} + 2 a^{2} - 5 a - 9\) , \( 2 a^{3} + 3 a^{2} - 12 a - 11\) , \( -2 a^{3} + 10 a^{2} + 20 a - 65\) , \( 33 a^{3} - 20 a^{2} - 234 a + 242\bigr] \)
${y}^2+\left(a^{3}+a^{2}-5a-3\right){x}{y}+\left(2a^{3}+3a^{2}-12a-11\right){y}={x}^{3}+\left(a^{3}+2a^{2}-5a-9\right){x}^{2}+\left(-2a^{3}+10a^{2}+20a-65\right){x}+33a^{3}-20a^{2}-234a+242$
59.2-d1
59.2-d
$1$
$1$
4.4.6125.1
$4$
$[4, 0]$
59.2
\( 59 \)
\( - 59^{3} \)
$11.64255$
$(3a^3+4a^2-18a-17)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$56.70901513$
0.724601215
\( -\frac{8193056918637954}{205379} a^{3} + \frac{14306032866590959}{205379} a^{2} + \frac{63063543446609149}{205379} a - \frac{120790269614565170}{205379} \)
\( \bigl[a^{3} + 2 a^{2} - 5 a - 7\) , \( a^{3} + 2 a^{2} - 6 a - 8\) , \( a\) , \( 14 a^{3} + 6 a^{2} - 59 a - 52\) , \( 29 a^{3} - 33 a^{2} - 59 a - 22\bigr] \)
${y}^2+\left(a^{3}+2a^{2}-5a-7\right){x}{y}+a{y}={x}^{3}+\left(a^{3}+2a^{2}-6a-8\right){x}^{2}+\left(14a^{3}+6a^{2}-59a-52\right){x}+29a^{3}-33a^{2}-59a-22$
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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.