Atkin-Lehner |
2+ 3- 5+ 7+ 41- |
Signs for the Atkin-Lehner involutions |
Class |
68880s |
Isogeny class |
Conductor |
68880 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
691200 |
Modular degree for the optimal curve |
Δ |
119190517031250000 = 24 · 33 · 510 · 75 · 412 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 7+ -2 2 2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-193971,-28442520] |
[a1,a2,a3,a4,a6] |
Generators |
[-283404:-2399766:1331] |
Generators of the group modulo torsion |
j |
50444797470919665664/7449407314453125 |
j-invariant |
L |
6.8014840506338 |
L(r)(E,1)/r! |
Ω |
0.22973851946039 |
Real period |
R |
9.8684424158447 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000948 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
34440b1 |
Quadratic twists by: -4 |