Atkin-Lehner |
2+ 3+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312z |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
13824 |
Modular degree for the optimal curve |
Δ |
-4435968 = -1 · 212 · 3 · 192 |
Discriminant |
Eigenvalues |
2+ 3+ -4 1 -2 -1 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-25,121] |
[a1,a2,a3,a4,a6] |
Generators |
[-1:12:1] [0:11:1] |
Generators of the group modulo torsion |
j |
-1216/3 |
j-invariant |
L |
7.1767231064146 |
L(r)(E,1)/r! |
Ω |
2.1700661615566 |
Real period |
R |
1.6535724194723 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000076 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69312by1 34656bh1 69312bk1 |
Quadratic twists by: -4 8 -19 |