Atkin-Lehner |
2+ 11- 67- |
Signs for the Atkin-Lehner involutions |
Class |
129712l |
Isogeny class |
Conductor |
129712 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
401280 |
Modular degree for the optimal curve |
Δ |
-27804919172272 = -1 · 24 · 1110 · 67 |
Discriminant |
Eigenvalues |
2+ 2 0 -4 11- 0 -2 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-48803,-4141234] |
[a1,a2,a3,a4,a6] |
Generators |
[5924103241635299826333345110:139143899946101501511044814738:9268492183994147444408375] |
Generators of the group modulo torsion |
j |
-30976000/67 |
j-invariant |
L |
7.2210400238832 |
L(r)(E,1)/r! |
Ω |
0.16058349385046 |
Real period |
R |
44.967510985953 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
64856c1 129712k1 |
Quadratic twists by: -4 -11 |