Atkin-Lehner |
2+ 5+ 11- 89- |
Signs for the Atkin-Lehner involutions |
Class |
78320l |
Isogeny class |
Conductor |
78320 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-34852400 = -1 · 24 · 52 · 11 · 892 |
Discriminant |
Eigenvalues |
2+ 0 5+ -2 11- 4 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,62,-213] |
[a1,a2,a3,a4,a6] |
Generators |
[67:552:1] |
Generators of the group modulo torsion |
j |
1647323136/2178275 |
j-invariant |
L |
4.6985631493765 |
L(r)(E,1)/r! |
Ω |
1.1017717484656 |
Real period |
R |
4.2645522117898 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000005469 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
39160k1 |
Quadratic twists by: -4 |