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
59.1-a1
59.1-a
$1$
$1$
4.4.6125.1
$4$
$[4, 0]$
59.1
\( 59 \)
\( - 59^{3} \)
$11.64255$
$(a^3+a^2-5a-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$175.2162663$
2.238831327
\( -\frac{573485304627}{205379} a^{3} - \frac{806332617709}{205379} a^{2} + \frac{3346741850839}{205379} a + \frac{2708257735800}{205379} \)
\( \bigl[2 a^{3} + 3 a^{2} - 12 a - 12\) , \( -a^{3} - a^{2} + 6 a + 4\) , \( a\) , \( 132 a^{3} + 160 a^{2} - 837 a - 663\) , \( 3307 a^{3} + 3992 a^{2} - 20951 a - 16480\bigr] \)
${y}^2+\left(2a^{3}+3a^{2}-12a-12\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}-a^{2}+6a+4\right){x}^{2}+\left(132a^{3}+160a^{2}-837a-663\right){x}+3307a^{3}+3992a^{2}-20951a-16480$
59.1-b1
59.1-b
$1$
$1$
4.4.6125.1
$4$
$[4, 0]$
59.1
\( 59 \)
\( - 59^{3} \)
$11.64255$
$(a^3+a^2-5a-2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 3 \)
$0.062194364$
$271.9299651$
2.593201710
\( -\frac{573485304627}{205379} a^{3} - \frac{806332617709}{205379} a^{2} + \frac{3346741850839}{205379} a + \frac{2708257735800}{205379} \)
\( \bigl[2 a^{3} + 3 a^{2} - 11 a - 11\) , \( a^{3} + a^{2} - 5 a - 3\) , \( a^{3} + a^{2} - 6 a - 4\) , \( 21 a^{3} + 29 a^{2} - 121 a - 99\) , \( 26 a^{3} + 36 a^{2} - 150 a - 124\bigr] \)
${y}^2+\left(2a^{3}+3a^{2}-11a-11\right){x}{y}+\left(a^{3}+a^{2}-6a-4\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-3\right){x}^{2}+\left(21a^{3}+29a^{2}-121a-99\right){x}+26a^{3}+36a^{2}-150a-124$
59.1-c1
59.1-c
$1$
$1$
4.4.6125.1
$4$
$[4, 0]$
59.1
\( 59 \)
\( - 59^{3} \)
$11.64255$
$(a^3+a^2-5a-2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 3 \)
$0.065073306$
$330.0357331$
3.293002336
\( \frac{67096438423877205}{205379} a^{3} + \frac{81001640358658630}{205379} a^{2} - \frac{425077720328492143}{205379} a - \frac{334381463093740074}{205379} \)
\( \bigl[2 a^{3} + 3 a^{2} - 12 a - 12\) , \( 2 a^{3} + 3 a^{2} - 11 a - 11\) , \( a^{3} + 2 a^{2} - 5 a - 7\) , \( 40 a^{3} + 50 a^{2} - 249 a - 200\) , \( -90 a^{3} - 108 a^{2} + 572 a + 448\bigr] \)
${y}^2+\left(2a^{3}+3a^{2}-12a-12\right){x}{y}+\left(a^{3}+2a^{2}-5a-7\right){y}={x}^{3}+\left(2a^{3}+3a^{2}-11a-11\right){x}^{2}+\left(40a^{3}+50a^{2}-249a-200\right){x}-90a^{3}-108a^{2}+572a+448$
59.1-d1
59.1-d
$1$
$1$
4.4.6125.1
$4$
$[4, 0]$
59.1
\( 59 \)
\( - 59^{3} \)
$11.64255$
$(a^3+a^2-5a-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$56.70901513$
0.724601215
\( \frac{67096438423877205}{205379} a^{3} + \frac{81001640358658630}{205379} a^{2} - \frac{425077720328492143}{205379} a - \frac{334381463093740074}{205379} \)
\( \bigl[2 a^{3} + 3 a^{2} - 11 a - 12\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} + a^{2} - 6 a - 3\) , \( 7 a^{3} + 34 a^{2} - 28 a - 189\) , \( -20 a^{3} + 94 a^{2} + 188 a - 672\bigr] \)
${y}^2+\left(2a^{3}+3a^{2}-11a-12\right){x}{y}+\left(a^{3}+a^{2}-6a-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(7a^{3}+34a^{2}-28a-189\right){x}-20a^{3}+94a^{2}+188a-672$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.