Atkin-Lehner |
2+ 3+ 5- 7- 73+ |
Signs for the Atkin-Lehner involutions |
Class |
61320j |
Isogeny class |
Conductor |
61320 |
Conductor |
∏ cp |
26 |
Product of Tamagawa factors cp |
deg |
643968 |
Modular degree for the optimal curve |
Δ |
196445566406250000 = 24 · 39 · 513 · 7 · 73 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 7- -3 -6 -3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-169240,-16173275] |
[a1,a2,a3,a4,a6] |
Generators |
[-270:3125:1] |
Generators of the group modulo torsion |
j |
33505441546231388416/12277847900390625 |
j-invariant |
L |
4.724810641896 |
L(r)(E,1)/r! |
Ω |
0.24261598158267 |
Real period |
R |
0.74901696517784 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998942 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122640r1 |
Quadratic twists by: -4 |