Atkin-Lehner |
2- 3+ 5+ 7- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
84420c |
Isogeny class |
Conductor |
84420 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
96768 |
Modular degree for the optimal curve |
Δ |
-180934009200 = -1 · 24 · 39 · 52 · 73 · 67 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7- 3 -7 2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1053,-24327] |
[a1,a2,a3,a4,a6] |
Generators |
[48:189:1] |
Generators of the group modulo torsion |
j |
-410012928/574525 |
j-invariant |
L |
6.2180917414705 |
L(r)(E,1)/r! |
Ω |
0.39870181556531 |
Real period |
R |
1.2996537551414 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000156 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
84420g1 |
Quadratic twists by: -3 |