Atkin-Lehner |
2+ 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
75712x |
Isogeny class |
Conductor |
75712 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
82944 |
Modular degree for the optimal curve |
Δ |
-325757845504 = -1 · 214 · 76 · 132 |
Discriminant |
Eigenvalues |
2+ 0 -1 7- -2 13+ -3 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-9308,346736] |
[a1,a2,a3,a4,a6] |
Generators |
[-107:343:1] [40:196:1] |
Generators of the group modulo torsion |
j |
-32209663824/117649 |
j-invariant |
L |
9.7666228996497 |
L(r)(E,1)/r! |
Ω |
0.96852643426725 |
Real period |
R |
0.84033353436566 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000038 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
75712bq1 4732d1 75712a1 |
Quadratic twists by: -4 8 13 |