Atkin-Lehner |
2+ 3- 11+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
120384z |
Isogeny class |
Conductor |
120384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
405504 |
Modular degree for the optimal curve |
Δ |
75512549376 = 212 · 36 · 113 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 2 -2 11+ -2 -6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-303444,64337760] |
[a1,a2,a3,a4,a6] |
Generators |
[190:3680:1] |
Generators of the group modulo torsion |
j |
1034836884153792/25289 |
j-invariant |
L |
6.7474183884642 |
L(r)(E,1)/r! |
Ω |
0.79106201731125 |
Real period |
R |
4.2647847047154 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000006882 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
120384bk1 60192v1 13376i1 |
Quadratic twists by: -4 8 -3 |