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
$1$
$1$
4.4.6125.1
$4$
$[4, 0]$
59.3
\( 59 \)
\( - 59^{3} \)
$11.64255$
$(a^2-3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$175.2162663$
2.238831327
\( \frac{13620701540}{205379} a^{3} - \frac{80549275383}{205379} a^{2} + \frac{151123103842}{205379} a - \frac{87084955041}{205379} \)
\( \bigl[a\) , \( a^{3} + a^{2} - 6 a - 3\) , \( a^{3} + 2 a^{2} - 6 a - 8\) , \( -124 a^{3} - 169 a^{2} + 715 a + 576\) , \( -3046 a^{3} - 4155 a^{2} + 17591 a + 14171\bigr] \)
${y}^2+a{x}{y}+\left(a^{3}+2a^{2}-6a-8\right){y}={x}^{3}+\left(a^{3}+a^{2}-6a-3\right){x}^{2}+\left(-124a^{3}-169a^{2}+715a+576\right){x}-3046a^{3}-4155a^{2}+17591a+14171$
59.3-b1
59.3-b
$1$
$1$
4.4.6125.1
$4$
$[4, 0]$
59.3
\( 59 \)
\( - 59^{3} \)
$11.64255$
$(a^2-3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 3 \)
$0.062194364$
$271.9299651$
2.593201710
\( \frac{13620701540}{205379} a^{3} - \frac{80549275383}{205379} a^{2} + \frac{151123103842}{205379} a - \frac{87084955041}{205379} \)
\( \bigl[a^{3} + 2 a^{2} - 5 a - 7\) , \( a^{2} + a - 5\) , \( a^{3} + a^{2} - 6 a - 4\) , \( 13 a^{3} + 17 a^{2} - 74 a - 56\) , \( 19 a^{3} + 25 a^{2} - 110 a - 87\bigr] \)
${y}^2+\left(a^{3}+2a^{2}-5a-7\right){x}{y}+\left(a^{3}+a^{2}-6a-4\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(13a^{3}+17a^{2}-74a-56\right){x}+19a^{3}+25a^{2}-110a-87$
59.3-c1
59.3-c
$1$
$1$
4.4.6125.1
$4$
$[4, 0]$
59.3
\( 59 \)
\( - 59^{3} \)
$11.64255$
$(a^2-3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 3 \)
$0.065073306$
$330.0357331$
3.293002336
\( -\frac{61785124339543268}{205379} a^{3} - \frac{84284214124772181}{205379} a^{2} + \frac{356805544102478183}{205379} a + \frac{287475920285668815}{205379} \)
\( \bigl[a\) , \( a^{3} + 2 a^{2} - 7 a - 7\) , \( 2 a^{3} + 3 a^{2} - 11 a - 12\) , \( -34 a^{3} - 44 a^{2} + 193 a + 154\) , \( 83 a^{3} + 115 a^{2} - 481 a - 391\bigr] \)
${y}^2+a{x}{y}+\left(2a^{3}+3a^{2}-11a-12\right){y}={x}^{3}+\left(a^{3}+2a^{2}-7a-7\right){x}^{2}+\left(-34a^{3}-44a^{2}+193a+154\right){x}+83a^{3}+115a^{2}-481a-391$
59.3-d1
59.3-d
$1$
$1$
4.4.6125.1
$4$
$[4, 0]$
59.3
\( 59 \)
\( - 59^{3} \)
$11.64255$
$(a^2-3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$56.70901513$
0.724601215
\( -\frac{61785124339543268}{205379} a^{3} - \frac{84284214124772181}{205379} a^{2} + \frac{356805544102478183}{205379} a + \frac{287475920285668815}{205379} \)
\( \bigl[a^{3} + 2 a^{2} - 5 a - 8\) , \( a^{2} - a - 3\) , \( a\) , \( 65 a^{3} + 80 a^{2} - 416 a - 328\) , \( 271 a^{3} + 327 a^{2} - 1725 a - 1356\bigr] \)
${y}^2+\left(a^{3}+2a^{2}-5a-8\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(65a^{3}+80a^{2}-416a-328\right){x}+271a^{3}+327a^{2}-1725a-1356$
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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.