Atkin-Lehner |
2- 5+ 7+ |
Signs for the Atkin-Lehner involutions |
Class |
78400gg |
Isogeny class |
Conductor |
78400 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
774144 |
Modular degree for the optimal curve |
Δ |
-472252497920000000 = -1 · 220 · 57 · 78 |
Discriminant |
Eigenvalues |
2- -1 5+ 7+ -6 -4 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,194367,-2376863] |
[a1,a2,a3,a4,a6] |
Generators |
[1479:-78400:27] [261:8128:1] |
Generators of the group modulo torsion |
j |
34391/20 |
j-invariant |
L |
8.1481267637323 |
L(r)(E,1)/r! |
Ω |
0.17491419574884 |
Real period |
R |
0.97049093235212 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998336 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
78400d1 19600bt1 15680db1 78400hr1 |
Quadratic twists by: -4 8 5 -7 |