Atkin-Lehner |
3- 5- 7+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
68355t |
Isogeny class |
Conductor |
68355 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
248832 |
Modular degree for the optimal curve |
Δ |
879930864658125 = 39 · 54 · 74 · 313 |
Discriminant |
Eigenvalues |
0 3- 5- 7+ -3 -4 3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-33222,-1842633] |
[a1,a2,a3,a4,a6] |
Generators |
[-1134:1081:8] [-133:472:1] |
Generators of the group modulo torsion |
j |
2316761595904/502723125 |
j-invariant |
L |
9.1773801665154 |
L(r)(E,1)/r! |
Ω |
0.35907790088151 |
Real period |
R |
0.17748741026802 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999965 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
22785i1 68355j1 |
Quadratic twists by: -3 -7 |