Atkin-Lehner |
2+ 7- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
111328h |
Isogeny class |
Conductor |
111328 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
172032 |
Modular degree for the optimal curve |
Δ |
-239499481088 = -1 · 212 · 77 · 71 |
Discriminant |
Eigenvalues |
2+ -1 0 7- 3 -1 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-29073,1917889] |
[a1,a2,a3,a4,a6] |
Generators |
[-56:1835:1] [75:392:1] |
Generators of the group modulo torsion |
j |
-5639752000/497 |
j-invariant |
L |
9.6906634451926 |
L(r)(E,1)/r! |
Ω |
0.94526202226855 |
Real period |
R |
1.2814784706489 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999164 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
111328q1 15904a1 |
Quadratic twists by: -4 -7 |