Atkin-Lehner |
2+ 3- 19- |
Signs for the Atkin-Lehner involutions |
Class |
51984s |
Isogeny class |
Conductor |
51984 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
172800 |
Modular degree for the optimal curve |
Δ |
-1334543355353088 = -1 · 211 · 36 · 197 |
Discriminant |
Eigenvalues |
2+ 3- 0 -3 2 -1 5 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-27075,2455522] |
[a1,a2,a3,a4,a6] |
Generators |
[-171:1444:1] |
Generators of the group modulo torsion |
j |
-31250/19 |
j-invariant |
L |
5.385359488383 |
L(r)(E,1)/r! |
Ω |
0.44633380437167 |
Real period |
R |
1.5082208191578 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000009 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
25992h1 5776c1 2736e1 |
Quadratic twists by: -4 -3 -19 |