Atkin-Lehner |
2+ 3+ 5- 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68970m |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-6058738620 = -1 · 22 · 32 · 5 · 116 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 2 11- -6 -8 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-2,3744] |
[a1,a2,a3,a4,a6] |
Generators |
[-5:63:1] |
Generators of the group modulo torsion |
j |
-1/3420 |
j-invariant |
L |
3.4995859454381 |
L(r)(E,1)/r! |
Ω |
1.068601769155 |
Real period |
R |
0.81873014938631 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003027 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
570h1 |
Quadratic twists by: -11 |