Atkin-Lehner |
2- 3+ 13- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
72384ci |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
86929920 |
Modular degree for the optimal curve |
Δ |
-1.3298599558646E+27 |
Discriminant |
Eigenvalues |
2- 3+ 3 -3 -2 13- -3 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-9346399329,347795556502977] |
[a1,a2,a3,a4,a6] |
Generators |
[-135720885:86614331336:3375] |
Generators of the group modulo torsion |
j |
-2755540349064140770138698691784/40584105098407543642983 |
j-invariant |
L |
4.9998268282671 |
L(r)(E,1)/r! |
Ω |
0.044069546096486 |
Real period |
R |
14.181638089814 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000171 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72384dq1 36192p1 |
Quadratic twists by: -4 8 |