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-a3
41.3-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
41.3
\( 41 \)
\( - 41^{2} \)
$1.16154$
$(3a^2-a-3)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.1
$1$
\( 2 \)
$1$
$169.7284207$
0.484938345
\( -\frac{6655766653200}{1681} a^{2} + \frac{3693705667625}{1681} a + \frac{14955417009784}{1681} \)
\( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( 4 a^{2} - 4 a - 8\) , \( -11 a^{2} + 7 a + 26\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(4a^{2}-4a-8\right){x}-11a^{2}+7a+26$
1681.5-a4
1681.5-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
1681.5
\( 41^{2} \)
\( - 41^{8} \)
$2.15691$
$(3a^2-a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.1
$1$
\( 2^{2} \)
$1.077567693$
$4.133512640$
1.908917005
\( -\frac{6655766653200}{1681} a^{2} + \frac{3693705667625}{1681} a + \frac{14955417009784}{1681} \)
\( \bigl[a\) , \( -a^{2} - a + 1\) , \( a^{2} + a - 2\) , \( 29 a^{2} - 75 a - 2\) , \( 29 a^{2} - 64 a - 45\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(29a^{2}-75a-2\right){x}+29a^{2}-64a-45$
2009.3-a4
2009.3-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
2009.3
\( 7^{2} \cdot 41 \)
\( - 7^{6} \cdot 41^{2} \)
$2.22194$
$(-a^2-a+2), (3a^2-a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.1
$1$
\( 2^{2} \)
$1$
$9.872075642$
1.410296520
\( -\frac{6655766653200}{1681} a^{2} + \frac{3693705667625}{1681} a + \frac{14955417009784}{1681} \)
\( \bigl[a^{2} - 2\) , \( a + 1\) , \( 0\) , \( 8 a^{2} - 24 a + 4\) , \( -7 a^{2} - 7 a - 7\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(8a^{2}-24a+4\right){x}-7a^{2}-7a-7$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.