Atkin-Lehner |
2+ 3- 5+ 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
127680cq |
Isogeny class |
Conductor |
127680 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
327680 |
Modular degree for the optimal curve |
Δ |
-25235992857600 = -1 · 210 · 32 · 52 · 78 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 7- -4 -6 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,2499,237699] |
[a1,a2,a3,a4,a6] |
Generators |
[-21:420:1] [14:525:1] |
Generators of the group modulo torsion |
j |
1684801439744/24644524275 |
j-invariant |
L |
13.484771345781 |
L(r)(E,1)/r! |
Ω |
0.49784097811142 |
Real period |
R |
1.6929064618381 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000003544 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
127680dh1 15960m1 |
Quadratic twists by: -4 8 |