Atkin-Lehner |
2+ 3+ 5+ 71- |
Signs for the Atkin-Lehner involutions |
Class |
85200l |
Isogeny class |
Conductor |
85200 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
40960 |
Modular degree for the optimal curve |
Δ |
-10224000000 = -1 · 210 · 32 · 56 · 71 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ -2 -2 -4 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,392,3712] |
[a1,a2,a3,a4,a6] |
Generators |
[12:-100:1] [-3:50:1] |
Generators of the group modulo torsion |
j |
415292/639 |
j-invariant |
L |
8.7786885568741 |
L(r)(E,1)/r! |
Ω |
0.87522907558425 |
Real period |
R |
1.2537701273997 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000092 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
42600bc1 3408d1 |
Quadratic twists by: -4 5 |