Atkin-Lehner |
2- 3- 5+ 13+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
69030bl |
Isogeny class |
Conductor |
69030 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
184320 |
Modular degree for the optimal curve |
Δ |
-3206573276400 = -1 · 24 · 311 · 52 · 13 · 592 |
Discriminant |
Eigenvalues |
2- 3- 5+ -4 -4 13+ 4 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-2948,106647] |
[a1,a2,a3,a4,a6] |
Generators |
[-57:323:1] [-37:423:1] |
Generators of the group modulo torsion |
j |
-3885442650361/4398591600 |
j-invariant |
L |
12.961915726826 |
L(r)(E,1)/r! |
Ω |
0.7227036960986 |
Real period |
R |
1.1209569527591 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23010d1 |
Quadratic twists by: -3 |