Atkin-Lehner |
3+ 5+ 7+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
69825d |
Isogeny class |
Conductor |
69825 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
1622880 |
Modular degree for the optimal curve |
Δ |
-1230752013668296875 = -1 · 314 · 56 · 74 · 193 |
Discriminant |
Eigenvalues |
-2 3+ 5+ 7+ 4 -4 -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,212742,37645418] |
[a1,a2,a3,a4,a6] |
Generators |
[1881:84199:1] |
Generators of the group modulo torsion |
j |
28383712415744/32806384371 |
j-invariant |
L |
2.7708520434798 |
L(r)(E,1)/r! |
Ω |
0.18199924436094 |
Real period |
R |
2.5374208297228 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000006021 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2793h1 69825cc1 |
Quadratic twists by: 5 -7 |