Atkin-Lehner |
2+ 3+ 7- 83- |
Signs for the Atkin-Lehner involutions |
Class |
83664k |
Isogeny class |
Conductor |
83664 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
36864 |
Modular degree for the optimal curve |
Δ |
1377444096 = 28 · 33 · 74 · 83 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7- 4 -2 8 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-279,-170] |
[a1,a2,a3,a4,a6] |
Generators |
[38:210:1] |
Generators of the group modulo torsion |
j |
347482224/199283 |
j-invariant |
L |
9.1780210519784 |
L(r)(E,1)/r! |
Ω |
1.2678425973964 |
Real period |
R |
1.8097713922668 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001436 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
41832a1 83664i1 |
Quadratic twists by: -4 -3 |