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
41.3-a1
41.3-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
41.3
\( 41 \)
\( - 41^{10} \)
$1.16154$
$(3a^2-a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.2
$1$
\( 2 \cdot 5 \)
$1$
$1.357827366$
0.484938345
\( \frac{174656123697499408263335}{13422659310152401} a^{2} + \frac{182915726357803972950650}{13422659310152401} a - \frac{115913951592431810832436}{13422659310152401} \)
\( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( -91 a^{2} + 101 a - 68\) , \( -646 a^{2} + 852 a - 304\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-91a^{2}+101a-68\right){x}-646a^{2}+852a-304$
1681.5-a1
1681.5-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
1681.5
\( 41^{2} \)
\( - 41^{16} \)
$2.15691$
$(3a^2-a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.2
$1$
\( 2^{2} \)
$5.387838465$
$0.826702528$
1.908917005
\( \frac{174656123697499408263335}{13422659310152401} a^{2} + \frac{182915726357803972950650}{13422659310152401} a - \frac{115913951592431810832436}{13422659310152401} \)
\( \bigl[a^{2} - 1\) , \( a^{2} - a - 1\) , \( a^{2} - 1\) , \( -1272 a^{2} - 1375 a - 299\) , \( 45529 a^{2} + 47686 a - 16832\bigr] \)
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(-1272a^{2}-1375a-299\right){x}+45529a^{2}+47686a-16832$
2009.3-a2
2009.3-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
2009.3
\( 7^{2} \cdot 41 \)
\( - 7^{6} \cdot 41^{10} \)
$2.22194$
$(-a^2-a+2), (3a^2-a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.2
$1$
\( 2^{2} \)
$1$
$9.872075642$
1.410296520
\( \frac{174656123697499408263335}{13422659310152401} a^{2} + \frac{182915726357803972950650}{13422659310152401} a - \frac{115913951592431810832436}{13422659310152401} \)
\( \bigl[a^{2} - 2\) , \( a + 1\) , \( 0\) , \( -1192 a^{2} + 1896 a - 631\) , \( 28308 a^{2} - 54292 a + 18578\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1192a^{2}+1896a-631\right){x}+28308a^{2}-54292a+18578$
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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.