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
53.4-a1
53.4-a
$2$
$3$
\(\Q(\zeta_{13})^+\)
$6$
$[6, 0]$
53.4
\( 53 \)
\( - 53^{3} \)
$75.80303$
$(a^3-2a-2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 3 \)
$0.001279191$
$60162.44104$
2.27340
\( -\frac{43252627634}{148877} a^{5} + \frac{53595700543}{148877} a^{4} + \frac{203435375839}{148877} a^{3} - \frac{221723599564}{148877} a^{2} - \frac{206277232132}{148877} a + \frac{179199457234}{148877} \)
\( \bigl[a^{4} - 3 a^{2} + 1\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + 2 a - 1\) , \( a^{2} + a - 2\) , \( a^{5} - a^{4} - 3 a^{3} + 4 a^{2} - a\) , \( a^{5} - a^{4} - 3 a^{3} + 4 a^{2} - 1\bigr] \)
${y}^2+\left(a^{4}-3a^{2}+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+2a-1\right){x}^{2}+\left(a^{5}-a^{4}-3a^{3}+4a^{2}-a\right){x}+a^{5}-a^{4}-3a^{3}+4a^{2}-1$
53.4-a2
53.4-a
$2$
$3$
\(\Q(\zeta_{13})^+\)
$6$
$[6, 0]$
53.4
\( 53 \)
\( -53 \)
$75.80303$
$(a^3-2a-2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$0.003837573$
$60162.44104$
2.27340
\( \frac{1239096528}{53} a^{5} + \frac{608694462}{53} a^{4} - \frac{5293780984}{53} a^{3} - \frac{2945412880}{53} a^{2} + \frac{3048957429}{53} a + \frac{831251952}{53} \)
\( \bigl[a^{5} - 4 a^{3} + 2 a + 1\) , \( a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + 3 a\) , \( a^{2} - 1\) , \( 2 a^{5} + 2 a^{4} - 7 a^{3} - 5 a^{2} + 5 a + 1\) , \( a^{5} + a^{4} - 2 a^{3} - a^{2} + a\bigr] \)
${y}^2+\left(a^{5}-4a^{3}+2a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{5}+a^{4}-4a^{3}-3a^{2}+3a\right){x}^{2}+\left(2a^{5}+2a^{4}-7a^{3}-5a^{2}+5a+1\right){x}+a^{5}+a^{4}-2a^{3}-a^{2}+a$
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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.