Atkin-Lehner |
3+ 5- 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
69825be |
Isogeny class |
Conductor |
69825 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-2619528515625 = -1 · 3 · 58 · 76 · 19 |
Discriminant |
Eigenvalues |
-1 3+ 5- 7- 3 0 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-19013,1004156] |
[a1,a2,a3,a4,a6] |
Generators |
[76:35:1] |
Generators of the group modulo torsion |
j |
-16539745/57 |
j-invariant |
L |
2.9604453093138 |
L(r)(E,1)/r! |
Ω |
0.81390741320215 |
Real period |
R |
1.8186622093785 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002251 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69825bq1 1425j1 |
Quadratic twists by: 5 -7 |