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
41.1-a1
41.1-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
41.1
\( 41 \)
\( - 41^{10} \)
$1.16154$
$(a^2+2a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.2
$1$
\( 2 \cdot 5 \)
$1$
$1.357827366$
0.484938345
\( \frac{182915726357803972950650}{13422659310152401} a^{2} - \frac{357571850055303381213985}{13422659310152401} a + \frac{50482569444763032743584}{13422659310152401} \)
\( \bigl[1\) , \( -a^{2} + 3\) , \( 1\) , \( 99 a^{2} - 10 a - 348\) , \( 952 a^{2} - 216 a - 2798\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(99a^{2}-10a-348\right){x}+952a^{2}-216a-2798$
41.1-a2
41.1-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
41.1
\( 41 \)
\( 41^{5} \)
$1.16154$
$(a^2+2a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.2
$1$
\( 5 \)
$1$
$2.715654732$
0.484938345
\( -\frac{1469483101129546552831}{115856201} a^{2} + \frac{815501597212588028076}{115856201} a + \frac{3301898555789100922576}{115856201} \)
\( \bigl[1\) , \( -a^{2} + 3\) , \( 1\) , \( 144 a^{2} - 75 a - 328\) , \( 1172 a^{2} - 646 a - 2650\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(144a^{2}-75a-328\right){x}+1172a^{2}-646a-2650$
41.1-a3
41.1-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
41.1
\( 41 \)
\( 41 \)
$1.16154$
$(a^2+2a-4)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.1
$1$
\( 1 \)
$1$
$339.4568415$
0.484938345
\( -\frac{968480}{41} a^{2} - \frac{734681}{41} a + \frac{589810}{41} \)
\( \bigl[1\) , \( -a^{2} + 3\) , \( 1\) , \( -a^{2} + 2\) , \( 0\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-a^{2}+2\right){x}$
41.1-a4
41.1-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
41.1
\( 41 \)
\( - 41^{2} \)
$1.16154$
$(a^2+2a-4)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.1
$1$
\( 2 \)
$1$
$169.7284207$
0.484938345
\( \frac{3693705667625}{1681} a^{2} + \frac{2962060985575}{1681} a - \frac{2049821964241}{1681} \)
\( \bigl[1\) , \( -a^{2} + 3\) , \( 1\) , \( -6 a^{2} + 7\) , \( 2 a^{2} + 4 a + 2\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-6a^{2}+7\right){x}+2a^{2}+4a+2$
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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.