Atkin-Lehner |
2+ 3- 5- 7+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
69090w |
Isogeny class |
Conductor |
69090 |
Conductor |
∏ cp |
54 |
Product of Tamagawa factors cp |
deg |
399168 |
Modular degree for the optimal curve |
Δ |
914441558625000 = 23 · 33 · 56 · 78 · 47 |
Discriminant |
Eigenvalues |
2+ 3- 5- 7+ 0 -1 0 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-30063,1378906] |
[a1,a2,a3,a4,a6] |
Generators |
[-850:15121:8] |
Generators of the group modulo torsion |
j |
521213404201/158625000 |
j-invariant |
L |
5.9020081990526 |
L(r)(E,1)/r! |
Ω |
0.46116435265545 |
Real period |
R |
2.1330096906871 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999996129 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
69090f1 |
Quadratic twists by: -7 |