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
41.2-a3
41.2-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
41.2
\( 41 \)
\( 41 \)
$1.16154$
$(2a^2-3a-4)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.1
$1$
\( 1 \)
$1$
$339.4568415$
0.484938345
\( -\frac{734681}{41} a^{2} + \frac{1703161}{41} a - \frac{612469}{41} \)
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( a\) , \( 0\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}$
1681.4-a2
1681.4-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
1681.4
\( 41^{2} \)
\( 41^{7} \)
$2.15691$
$(2a^2-3a-4)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.1
$1$
\( 2^{2} \)
$0.538783846$
$8.267025280$
1.908917005
\( -\frac{734681}{41} a^{2} + \frac{1703161}{41} a - \frac{612469}{41} \)
\( \bigl[a^{2} - 2\) , \( -a^{2} - a + 2\) , \( a^{2} - 2\) , \( -8 a^{2} - 6 a + 4\) , \( 10 a^{2} + 6 a - 10\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-8a^{2}-6a+4\right){x}+10a^{2}+6a-10$
2009.2-a3
2009.2-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
2009.2
\( 7^{2} \cdot 41 \)
\( 7^{6} \cdot 41 \)
$2.22194$
$(-a^2-a+2), (2a^2-3a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.1
$1$
\( 2 \)
$1$
$19.74415128$
1.410296520
\( -\frac{734681}{41} a^{2} + \frac{1703161}{41} a - \frac{612469}{41} \)
\( \bigl[a^{2} + a - 1\) , \( a^{2} - a - 2\) , \( a^{2} + a - 2\) , \( -4 a^{2} - 2 a + 3\) , \( -3 a^{2} - 3 a\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-4a^{2}-2a+3\right){x}-3a^{2}-3a$
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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.