Atkin-Lehner |
3+ 7+ 13- 31- |
Signs for the Atkin-Lehner involutions |
Class |
8463b |
Isogeny class |
Conductor |
8463 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
3840 |
Modular degree for the optimal curve |
Δ |
-5075946603 = -1 · 32 · 72 · 135 · 31 |
Discriminant |
Eigenvalues |
0 3+ 0 7+ 3 13- 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,247,-3169] |
[a1,a2,a3,a4,a6] |
Generators |
[13:45:1] |
Generators of the group modulo torsion |
j |
1659797504000/5075946603 |
j-invariant |
L |
2.8585133670217 |
L(r)(E,1)/r! |
Ω |
0.69821117750962 |
Real period |
R |
0.20470263575681 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
25389f1 59241p1 110019j1 |
Quadratic twists by: -3 -7 13 |