Atkin-Lehner |
3+ 5- 31- 41- |
Signs for the Atkin-Lehner involutions |
Class |
19065g |
Isogeny class |
Conductor |
19065 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
144384 |
Modular degree for the optimal curve |
Δ |
-13113199700655375 = -1 · 3 · 53 · 318 · 41 |
Discriminant |
Eigenvalues |
-1 3+ 5- 0 -4 -2 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-307520,65741120] |
[a1,a2,a3,a4,a6] |
Generators |
[-362:11573:1] [134:5125:1] |
Generators of the group modulo torsion |
j |
-3216206300355197383681/13113199700655375 |
j-invariant |
L |
4.3276615558472 |
L(r)(E,1)/r! |
Ω |
0.400429715096 |
Real period |
R |
7.2050289854392 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
57195m1 95325z1 |
Quadratic twists by: -3 5 |