Atkin-Lehner |
2- 3- 7+ 103+ |
Signs for the Atkin-Lehner involutions |
Class |
51912o |
Isogeny class |
Conductor |
51912 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
311808 |
Modular degree for the optimal curve |
Δ |
-31838968076893488 = -1 · 24 · 313 · 76 · 1032 |
Discriminant |
Eigenvalues |
2- 3- -2 7+ -2 2 -4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-99426,-14809219] |
[a1,a2,a3,a4,a6] |
Generators |
[18434:876015:8] |
Generators of the group modulo torsion |
j |
-9319145753417728/2729678333067 |
j-invariant |
L |
4.0990736634106 |
L(r)(E,1)/r! |
Ω |
0.13242769976316 |
Real period |
R |
3.8691618810978 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000025 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
103824r1 17304a1 |
Quadratic twists by: -4 -3 |