Atkin-Lehner |
2- 3+ 7- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
111552cn |
Isogeny class |
Conductor |
111552 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-296082210816 = -1 · 221 · 35 · 7 · 83 |
Discriminant |
Eigenvalues |
2- 3+ -3 7- 1 -2 -1 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-897,28449] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:192:1] |
Generators of the group modulo torsion |
j |
-304821217/1129464 |
j-invariant |
L |
4.5625829056306 |
L(r)(E,1)/r! |
Ω |
0.84977144155829 |
Real period |
R |
1.3422970813454 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000005202 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
111552bm1 27888bm1 |
Quadratic twists by: -4 8 |