Atkin-Lehner |
2- 3- 7- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
84966dx |
Isogeny class |
Conductor |
84966 |
Conductor |
∏ cp |
324 |
Product of Tamagawa factors cp |
deg |
653184 |
Modular degree for the optimal curve |
Δ |
-342647317587456 = -1 · 29 · 39 · 76 · 172 |
Discriminant |
Eigenvalues |
2- 3- -3 7- -3 -2 17+ -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-78597,8521281] |
[a1,a2,a3,a4,a6] |
Generators |
[144:369:1] [-318:1335:1] |
Generators of the group modulo torsion |
j |
-1579268174113/10077696 |
j-invariant |
L |
15.733788518414 |
L(r)(E,1)/r! |
Ω |
0.54285437299725 |
Real period |
R |
0.089455069518781 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999809 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
1734j1 84966dj1 |
Quadratic twists by: -7 17 |