Atkin-Lehner |
2+ 3- 17+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
12648c |
Isogeny class |
Conductor |
12648 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
5760 |
Modular degree for the optimal curve |
Δ |
-1290096 = -1 · 24 · 32 · 172 · 31 |
Discriminant |
Eigenvalues |
2+ 3- -3 -5 -2 2 17+ -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-492,4041] |
[a1,a2,a3,a4,a6] |
Generators |
[-24:51:1] [3:51:1] |
Generators of the group modulo torsion |
j |
-824862293248/80631 |
j-invariant |
L |
5.9677623342857 |
L(r)(E,1)/r! |
Ω |
2.6036375189803 |
Real period |
R |
0.28651080895388 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
25296c1 101184d1 37944n1 |
Quadratic twists by: -4 8 -3 |