Atkin-Lehner |
3+ 41+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
8241a |
Isogeny class |
Conductor |
8241 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
35280 |
Modular degree for the optimal curve |
Δ |
-20426042743803 = -1 · 32 · 412 · 675 |
Discriminant |
Eigenvalues |
0 3+ -2 -4 0 6 -5 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-38349,2911529] |
[a1,a2,a3,a4,a6] |
Generators |
[-199:1619:1] [111:100:1] |
Generators of the group modulo torsion |
j |
-6237307678681464832/20426042743803 |
j-invariant |
L |
3.6624713646025 |
L(r)(E,1)/r! |
Ω |
0.68573479299863 |
Real period |
R |
0.2670472172331 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999996 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
24723f1 |
Quadratic twists by: -3 |