Atkin-Lehner |
3+ 19- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
31407b |
Isogeny class |
Conductor |
31407 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
3456 |
Modular degree for the optimal curve |
Δ |
282663 = 33 · 192 · 29 |
Discriminant |
Eigenvalues |
-1 3+ 2 -4 -2 -2 3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-17,-16] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:4:1] [-1:1:1] |
Generators of the group modulo torsion |
j |
1510633/783 |
j-invariant |
L |
4.8224032577743 |
L(r)(E,1)/r! |
Ω |
2.4872301235828 |
Real period |
R |
1.9388649293238 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000004 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
94221l1 31407c1 |
Quadratic twists by: -3 -19 |