Atkin-Lehner |
2- 3- 7- 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
84084v |
Isogeny class |
Conductor |
84084 |
Conductor |
∏ cp |
195 |
Product of Tamagawa factors cp |
deg |
786240 |
Modular degree for the optimal curve |
Δ |
617713639662175056 = 24 · 313 · 72 · 113 · 135 |
Discriminant |
Eigenvalues |
2- 3- -1 7- 11+ 13- -1 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-212921,336048] |
[a1,a2,a3,a4,a6] |
Generators |
[-101:-4563:1] |
Generators of the group modulo torsion |
j |
1361649029162254336/787900050589509 |
j-invariant |
L |
7.3278146899527 |
L(r)(E,1)/r! |
Ω |
0.24447648546892 |
Real period |
R |
0.15371023025083 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997897 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
84084a1 |
Quadratic twists by: -7 |