Atkin-Lehner |
2- 3- 5- 7+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
78120bj |
Isogeny class |
Conductor |
78120 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
331776 |
Modular degree for the optimal curve |
Δ |
-217040796000000 = -1 · 28 · 36 · 56 · 74 · 31 |
Discriminant |
Eigenvalues |
2- 3- 5- 7+ 4 4 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-73407,7687906] |
[a1,a2,a3,a4,a6] |
Generators |
[137:-450:1] |
Generators of the group modulo torsion |
j |
-234405957659344/1162984375 |
j-invariant |
L |
7.6180455616088 |
L(r)(E,1)/r! |
Ω |
0.56381780490328 |
Real period |
R |
0.56298073993337 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002362 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8680e1 |
Quadratic twists by: -3 |