Atkin-Lehner |
2- 7- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
72128bk |
Isogeny class |
Conductor |
72128 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
688128 |
Modular degree for the optimal curve |
Δ |
-943968651931648 = -1 · 212 · 77 · 234 |
Discriminant |
Eigenvalues |
2- 2 -4 7- -4 4 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-68665,7104441] |
[a1,a2,a3,a4,a6] |
Generators |
[201:1176:1] |
Generators of the group modulo torsion |
j |
-74299881664/1958887 |
j-invariant |
L |
6.7405132662513 |
L(r)(E,1)/r! |
Ω |
0.49503717781513 |
Real period |
R |
1.7020219813595 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000592 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72128cg1 36064a1 10304v1 |
Quadratic twists by: -4 8 -7 |