Atkin-Lehner |
2- 3+ 5+ 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
129360dz |
Isogeny class |
Conductor |
129360 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
3096576 |
Modular degree for the optimal curve |
Δ |
-7199961583288320000 = -1 · 218 · 32 · 54 · 79 · 112 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7- 11+ 4 -2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,482144,7718656] |
[a1,a2,a3,a4,a6] |
Generators |
[496:19200:1] |
Generators of the group modulo torsion |
j |
74991286313/43560000 |
j-invariant |
L |
5.2969722755622 |
L(r)(E,1)/r! |
Ω |
0.14181943266376 |
Real period |
R |
2.334382149616 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000457429 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
16170ca1 129360hr1 |
Quadratic twists by: -4 -7 |