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
71.3-a1
71.3-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
71.3
\( 71 \)
\( - 71^{5} \)
$1.27286$
$(a^2-6)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.2
$1$
\( 5 \)
$1$
$3.289607277$
0.587429871
\( -\frac{925759129064909928}{1804229351} a^{2} + \frac{385959155459705697}{1804229351} a + \frac{2310445605654755654}{1804229351} \)
\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( 4 a^{2} - 10 a - 44\) , \( -32 a^{2} - 61 a - 73\bigr] \)
${y}^2+{x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(4a^{2}-10a-44\right){x}-32a^{2}-61a-73$
71.3-a2
71.3-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
71.3
\( 71 \)
\( -71 \)
$1.27286$
$(a^2-6)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.1
$1$
\( 1 \)
$1$
$411.2009097$
0.587429871
\( \frac{2121}{71} a^{2} - \frac{713073}{71} a + \frac{1242209}{71} \)
\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( -a^{2} + 1\) , \( 0\bigr] \)
${y}^2+{x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-a^{2}+1\right){x}$
71.3-a3
71.3-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
71.3
\( 71 \)
\( - 71^{2} \)
$1.27286$
$(a^2-6)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.1
$1$
\( 2 \)
$1$
$205.6004548$
0.587429871
\( \frac{841196669387}{5041} a^{2} - \frac{1885779500418}{5041} a + \frac{672641959002}{5041} \)
\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( -11 a^{2} - 5 a + 6\) , \( 18 a^{2} + 12 a - 9\bigr] \)
${y}^2+{x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-11a^{2}-5a+6\right){x}+18a^{2}+12a-9$
71.3-a4
71.3-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
71.3
\( 71 \)
\( - 71^{10} \)
$1.27286$
$(a^2-6)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.2
$1$
\( 2 \cdot 5 \)
$1$
$1.644803638$
0.587429871
\( \frac{1128735985778740212430417}{3255243551009881201} a^{2} + \frac{808193592087701284035551}{3255243551009881201} a - \frac{697032567862883246911701}{3255243551009881201} \)
\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( -221 a^{2} - 190 a + 81\) , \( -2926 a^{2} - 2384 a + 1532\bigr] \)
${y}^2+{x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-221a^{2}-190a+81\right){x}-2926a^{2}-2384a+1532$
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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.