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
\( \frac{182915726357803972950650}{13422659310152401} a^{2} - \frac{357571850055303381213985}{13422659310152401} a + \frac{50482569444763032743584}{13422659310152401} \)
\( \bigl[1\) , \( -a^{2} + 3\) , \( 1\) , \( 99 a^{2} - 10 a - 348\) , \( 952 a^{2} - 216 a - 2798\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(99a^{2}-10a-348\right){x}+952a^{2}-216a-2798$
1681.6-a3
1681.6-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
1681.6
\( 41^{2} \)
\( - 41^{16} \)
$2.15691$
$(a^2+2a-4)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.2
$1$
\( 2^{2} \)
$5.387838465$
$0.826702528$
1.908917005
\( \frac{182915726357803972950650}{13422659310152401} a^{2} - \frac{357571850055303381213985}{13422659310152401} a + \frac{50482569444763032743584}{13422659310152401} \)
\( \bigl[a + 1\) , \( -a^{2} - a + 2\) , \( a + 1\) , \( -1375 a^{2} + 2645 a - 1468\) , \( 47686 a^{2} - 93216 a + 26540\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-1375a^{2}+2645a-1468\right){x}+47686a^{2}-93216a+26540$
2009.1-a1
2009.1-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
2009.1
\( 7^{2} \cdot 41 \)
\( - 7^{6} \cdot 41^{10} \)
$2.22194$
$(-a^2-a+2), (a^2+2a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.2
$1$
\( 2^{2} \)
$1$
$9.872075642$
1.410296520
\( \frac{182915726357803972950650}{13422659310152401} a^{2} - \frac{357571850055303381213985}{13422659310152401} a + \frac{50482569444763032743584}{13422659310152401} \)
\( \bigl[a\) , \( a^{2} - a - 3\) , \( a\) , \( 1893 a^{2} - 702 a - 4908\) , \( -56187 a^{2} + 26687 a + 134396\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(1893a^{2}-702a-4908\right){x}-56187a^{2}+26687a+134396$
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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.