Atkin-Lehner |
3+ 5- 7- 13+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
69615d |
Isogeny class |
Conductor |
69615 |
Conductor |
∏ cp |
40 |
Product of Tamagawa factors cp |
deg |
52480 |
Modular degree for the optimal curve |
Δ |
-44771146875 = -1 · 33 · 55 · 74 · 13 · 17 |
Discriminant |
Eigenvalues |
0 3+ 5- 7- -6 13+ 17+ -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,828,4420] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:52:1] |
Generators of the group modulo torsion |
j |
2325149908992/1658190625 |
j-invariant |
L |
4.1253254293186 |
L(r)(E,1)/r! |
Ω |
0.72202186035337 |
Real period |
R |
0.14283935349699 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999998972 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69615b1 |
Quadratic twists by: -3 |