Atkin-Lehner |
2+ 3- 7+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
76608bj |
Isogeny class |
Conductor |
76608 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
245760 |
Modular degree for the optimal curve |
Δ |
172935198277632 = 220 · 311 · 72 · 19 |
Discriminant |
Eigenvalues |
2+ 3- -2 7+ -2 -2 4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-52716,-4615504] |
[a1,a2,a3,a4,a6] |
Generators |
[-140:144:1] [-136:196:1] |
Generators of the group modulo torsion |
j |
84778086457/904932 |
j-invariant |
L |
9.2787314419743 |
L(r)(E,1)/r! |
Ω |
0.31527823011374 |
Real period |
R |
7.3575738472494 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000007 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
76608fs1 2394l1 25536b1 |
Quadratic twists by: -4 8 -3 |