Atkin-Lehner |
2+ 3- 7- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
78078bk |
Isogeny class |
Conductor |
78078 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
737280 |
Modular degree for the optimal curve |
Δ |
-13308678989109504 = -1 · 28 · 32 · 710 · 112 · 132 |
Discriminant |
Eigenvalues |
2+ 3- -1 7- 11+ 13+ -3 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-130719,-19029710] |
[a1,a2,a3,a4,a6] |
Generators |
[647:-13260:1] |
Generators of the group modulo torsion |
j |
-1461666798564168001/78749579817216 |
j-invariant |
L |
5.0694572672844 |
L(r)(E,1)/r! |
Ω |
0.12514887328172 |
Real period |
R |
0.50634267932941 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004503 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
78078cz1 |
Quadratic twists by: 13 |