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-b1
41.1-b
$1$
$1$
4.4.5125.1
$4$
$[4, 0]$
41.1
\( 41 \)
\( 41^{4} \)
$10.17615$
$(a^3-a^2-4a-3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2^{2} \)
$0.485050994$
$21.35387477$
2.314926137
\( \frac{71073792}{1681} a^{3} - \frac{64847872}{1681} a^{2} - \frac{296812544}{1681} a - \frac{149258240}{1681} \)
\( \bigl[0\) , \( -a^{3} + a^{2} + 4 a\) , \( a^{3} - a^{2} - 3 a\) , \( -9 a^{3} - 7 a^{2} + 37 a + 39\) , \( -31 a^{3} - 23 a^{2} + 126 a + 126\bigr] \)
${y}^2+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a\right){x}^{2}+\left(-9a^{3}-7a^{2}+37a+39\right){x}-31a^{3}-23a^{2}+126a+126$
41.1-e1
41.1-e
$1$
$1$
4.4.5125.1
$4$
$[4, 0]$
41.1
\( 41 \)
\( 41^{4} \)
$10.17615$
$(a^3-a^2-4a-3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2^{2} \)
$0.009312090$
$1120.903857$
2.332859573
\( \frac{71073792}{1681} a^{3} - \frac{64847872}{1681} a^{2} - \frac{296812544}{1681} a - \frac{149258240}{1681} \)
\( \bigl[0\) , \( -a^{2} + 4\) , \( a^{2} - 3\) , \( 6 a^{3} - 20 a^{2} - 3 a + 39\) , \( -9 a^{3} + 32 a^{2} - 5 a - 48\bigr] \)
${y}^2+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(6a^{3}-20a^{2}-3a+39\right){x}-9a^{3}+32a^{2}-5a-48$
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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.