Atkin-Lehner |
3- 7+ 13+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
78351k |
Isogeny class |
Conductor |
78351 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
150528 |
Modular degree for the optimal curve |
Δ |
248883753573 = 34 · 78 · 13 · 41 |
Discriminant |
Eigenvalues |
-2 3- 2 7+ -3 13+ 0 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-2172,-31426] |
[a1,a2,a3,a4,a6] |
Generators |
[-36:37:1] [-33:73:1] |
Generators of the group modulo torsion |
j |
196661248/43173 |
j-invariant |
L |
7.5090329245854 |
L(r)(E,1)/r! |
Ω |
0.71024202913308 |
Real period |
R |
0.88104155774922 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998255 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
78351i1 |
Quadratic twists by: -7 |