Atkin-Lehner |
3+ 5+ 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
69825y |
Isogeny class |
Conductor |
69825 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
24192 |
Modular degree for the optimal curve |
Δ |
-11940075 = -1 · 33 · 52 · 72 · 192 |
Discriminant |
Eigenvalues |
-2 3+ 5+ 7- 0 2 -6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-58,258] |
[a1,a2,a3,a4,a6] |
Generators |
[6:9:1] |
Generators of the group modulo torsion |
j |
-17920000/9747 |
j-invariant |
L |
2.6954310865767 |
L(r)(E,1)/r! |
Ω |
2.0987082558982 |
Real period |
R |
0.64216431155892 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000007245 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69825cj1 69825bi1 |
Quadratic twists by: 5 -7 |