Atkin-Lehner |
2- 5- 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
86240bx |
Isogeny class |
Conductor |
86240 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
85248 |
Modular degree for the optimal curve |
Δ |
4312000000 = 29 · 56 · 72 · 11 |
Discriminant |
Eigenvalues |
2- -3 5- 7- 11+ -1 -4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-427,1246] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:-50:1] [2:20:1] |
Generators of the group modulo torsion |
j |
343195272/171875 |
j-invariant |
L |
7.2983141795232 |
L(r)(E,1)/r! |
Ω |
1.2239788030231 |
Real period |
R |
0.4968981871263 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998417 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
86240r1 86240s1 |
Quadratic twists by: -4 -7 |