Atkin-Lehner |
2+ 3+ 5+ 11+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
81840c |
Isogeny class |
Conductor |
81840 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
28672 |
Modular degree for the optimal curve |
Δ |
-121777920 = -1 · 28 · 32 · 5 · 11 · 312 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 4 11+ 2 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,124,0] |
[a1,a2,a3,a4,a6] |
Generators |
[9:42:1] |
Generators of the group modulo torsion |
j |
817036976/475695 |
j-invariant |
L |
6.33434383039 |
L(r)(E,1)/r! |
Ω |
1.1229132196045 |
Real period |
R |
2.8204957067168 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.00000000009 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
40920bf1 |
Quadratic twists by: -4 |