Atkin-Lehner |
2+ 3- 7- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
69384m |
Isogeny class |
Conductor |
69384 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
331776 |
Modular degree for the optimal curve |
Δ |
60683431377744 = 24 · 33 · 79 · 592 |
Discriminant |
Eigenvalues |
2+ 3- -2 7- -2 4 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-150299,-22474614] |
[a1,a2,a3,a4,a6] |
Generators |
[625:11319:1] |
Generators of the group modulo torsion |
j |
199474163304448/32237541 |
j-invariant |
L |
6.5756490340194 |
L(r)(E,1)/r! |
Ω |
0.242473623632 |
Real period |
R |
2.2599190157495 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999994764 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
9912a1 |
Quadratic twists by: -7 |