Atkin-Lehner |
2+ 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
75712bm |
Isogeny class |
Conductor |
75712 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
1161216 |
Modular degree for the optimal curve |
Δ |
-11284115006947328 = -1 · 219 · 73 · 137 |
Discriminant |
Eigenvalues |
2+ -3 -4 7- 1 13+ 0 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,35828,-4394000] |
[a1,a2,a3,a4,a6] |
Generators |
[286:-5408:1] [117:1183:1] |
Generators of the group modulo torsion |
j |
4019679/8918 |
j-invariant |
L |
5.1803283285197 |
L(r)(E,1)/r! |
Ω |
0.20938990292692 |
Real period |
R |
0.51541886849615 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000283 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
75712ci1 2366g1 5824g1 |
Quadratic twists by: -4 8 13 |