Atkin-Lehner |
3+ 5+ 7+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
83475c |
Isogeny class |
Conductor |
83475 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
741312 |
Modular degree for the optimal curve |
Δ |
-51568632024271425 = -1 · 39 · 52 · 711 · 53 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 7+ -5 -2 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-271595,-55495988] |
[a1,a2,a3,a4,a6] |
Generators |
[1228654910:39463805011:941192] |
Generators of the group modulo torsion |
j |
-4502525935581315/104798317379 |
j-invariant |
L |
3.1126678994566 |
L(r)(E,1)/r! |
Ω |
0.1044218733684 |
Real period |
R |
14.904290636112 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001789 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
83475f1 83475o1 |
Quadratic twists by: -3 5 |