Atkin-Lehner |
2+ 7+ 17- 41- |
Signs for the Atkin-Lehner involutions |
Class |
68306c |
Isogeny class |
Conductor |
68306 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
1201824 |
Modular degree for the optimal curve |
Δ |
920014705274126336 = 239 · 74 · 17 · 41 |
Discriminant |
Eigenvalues |
2+ -2 -1 7+ -2 -2 17- 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-1017119,392034738] |
[a1,a2,a3,a4,a6] |
Generators |
[-678:28089:1] |
Generators of the group modulo torsion |
j |
48467011259935500169/383179802279936 |
j-invariant |
L |
2.039370290708 |
L(r)(E,1)/r! |
Ω |
0.28107686318246 |
Real period |
R |
7.255560871629 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001379 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68306f1 |
Quadratic twists by: -7 |