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-a4
41.2-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
41.2
\( 41 \)
\( 41^{5} \)
$1.16154$
$(2a^2-3a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.2
$1$
\( 5 \)
$1$
$2.715654732$
0.484938345
\( \frac{815501597212588028076}{115856201} a^{2} + \frac{653981503916958524755}{115856201} a - \frac{452569243682580211162}{115856201} \)
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -75 a^{2} - 69 a + 35\) , \( -646 a^{2} - 526 a + 340\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-75a^{2}-69a+35\right){x}-646a^{2}-526a+340$
1681.4-a4
1681.4-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
1681.4
\( 41^{2} \)
\( 41^{11} \)
$2.15691$
$(2a^2-3a-4)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.2
$1$
\( 2^{2} \)
$2.693919232$
$1.653405056$
1.908917005
\( \frac{815501597212588028076}{115856201} a^{2} + \frac{653981503916958524755}{115856201} a - \frac{452569243682580211162}{115856201} \)
\( \bigl[a^{2} + a - 2\) , \( -a^{2} + a + 1\) , \( a^{2} + a - 2\) , \( 70 a^{2} - 267 a - 313\) , \( -2618 a^{2} - 707 a + 4273\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(70a^{2}-267a-313\right){x}-2618a^{2}-707a+4273$
2009.2-a4
2009.2-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
2009.2
\( 7^{2} \cdot 41 \)
\( 7^{6} \cdot 41^{5} \)
$2.22194$
$(-a^2-a+2), (2a^2-3a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.2
$1$
\( 2 \)
$1$
$19.74415128$
1.410296520
\( \frac{815501597212588028076}{115856201} a^{2} + \frac{653981503916958524755}{115856201} a - \frac{452569243682580211162}{115856201} \)
\( \bigl[a^{2} + a - 1\) , \( a^{2} - a - 2\) , \( a^{2} + a - 2\) , \( -1144 a^{2} - 957 a + 588\) , \( 29910 a^{2} + 24148 a - 16393\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-1144a^{2}-957a+588\right){x}+29910a^{2}+24148a-16393$
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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.