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-a1
41.2-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
41.2
\( 41 \)
\( - 41^{10} \)
$1.16154$
$(2a^2-3a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.2
$1$
\( 2 \cdot 5 \)
$1$
$1.357827366$
0.484938345
\( -\frac{357571850055303381213985}{13422659310152401} a^{2} + \frac{174656123697499408263335}{13422659310152401} a + \frac{773885872215674359858869}{13422659310152401} \)
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -10 a^{2} - 89 a - 140\) , \( -216 a^{2} - 736 a - 678\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-10a^{2}-89a-140\right){x}-216a^{2}-736a-678$
41.2-a2
41.2-a
$4$
$10$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
41.2
\( 41 \)
\( - 41^{2} \)
$1.16154$
$(2a^2-3a-4)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.1
$1$
\( 2 \)
$1$
$169.7284207$
0.484938345
\( \frac{2962060985575}{1681} a^{2} - \frac{6655766653200}{1681} a + \frac{2375528385434}{1681} \)
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 6 a - 5\) , \( 4 a^{2} - 6 a + 2\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-5\right){x}+4a^{2}-6a+2$
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
\( -\frac{734681}{41} a^{2} + \frac{1703161}{41} a - \frac{612469}{41} \)
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( a\) , \( 0\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}$
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
\( \frac{815501597212588028076}{115856201} a^{2} + \frac{653981503916958524755}{115856201} a - \frac{452569243682580211162}{115856201} \)
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -75 a^{2} - 69 a + 35\) , \( -646 a^{2} - 526 a + 340\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-75a^{2}-69a+35\right){x}-646a^{2}-526a+340$
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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.