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
71.2-a1
71.2-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
71.2
\( 71 \)
\( - 71^{10} \)
$1.27286$
$(-3a^2+4a+5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.2
$1$
\( 2 \cdot 5 \)
$1$
$1.644803638$
0.587429871
\( -\frac{1936929577866441496465968}{3255243551009881201} a^{2} + \frac{1128735985778740212430417}{3255243551009881201} a + \frac{4305562573648739958450652}{3255243551009881201} \)
\( \bigl[1\) , \( -a^{2} + a + 1\) , \( a^{2} + a - 2\) , \( 410 a^{2} - 221 a - 960\) , \( 5309 a^{2} - 2926 a - 12013\bigr] \)
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(410a^{2}-221a-960\right){x}+5309a^{2}-2926a-12013$
71.2-a2
71.2-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
71.2
\( 71 \)
\( - 71^{5} \)
$1.27286$
$(-3a^2+4a+5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.2
$1$
\( 5 \)
$1$
$3.289607277$
0.587429871
\( \frac{539799973605204231}{1804229351} a^{2} - \frac{925759129064909928}{1804229351} a + \frac{305086529379437264}{1804229351} \)
\( \bigl[1\) , \( -a^{2} + a + 1\) , \( a^{2} + a - 2\) , \( 5 a^{2} + 4 a - 50\) , \( 92 a^{2} - 32 a - 290\bigr] \)
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(5a^{2}+4a-50\right){x}+92a^{2}-32a-290$
71.2-a3
71.2-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
71.2
\( 71 \)
\( - 71^{2} \)
$1.27286$
$(-3a^2+4a+5)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.1
$1$
\( 2 \)
$1$
$205.6004548$
0.587429871
\( \frac{1044582831031}{5041} a^{2} + \frac{841196669387}{5041} a - \frac{575327033673}{5041} \)
\( \bigl[1\) , \( -a^{2} + a + 1\) , \( a^{2} + a - 2\) , \( 15 a^{2} - 11 a - 35\) , \( -31 a^{2} + 18 a + 70\bigr] \)
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(15a^{2}-11a-35\right){x}-31a^{2}+18a+70$
71.2-a4
71.2-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
71.2
\( 71 \)
\( -71 \)
$1.27286$
$(-3a^2+4a+5)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.1
$1$
\( 1 \)
$1$
$411.2009097$
0.587429871
\( \frac{710952}{71} a^{2} + \frac{2121}{71} a - \frac{177574}{71} \)
\( \bigl[1\) , \( -a^{2} + a + 1\) , \( a^{2} + a - 2\) , \( -a\) , \( -a^{2} + 1\bigr] \)
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}-a{x}-a^{2}+1$
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.