Atkin-Lehner |
3- 5+ 7- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
61005p |
Isogeny class |
Conductor |
61005 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-25632775875 = -1 · 3 · 53 · 77 · 83 |
Discriminant |
Eigenvalues |
0 3- 5+ 7- -2 -6 -6 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-7611,253166] |
[a1,a2,a3,a4,a6] |
Generators |
[44:73:1] |
Generators of the group modulo torsion |
j |
-414493474816/217875 |
j-invariant |
L |
3.8686470792787 |
L(r)(E,1)/r! |
Ω |
1.1761973170846 |
Real period |
R |
0.82227850360459 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998306 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8715f1 |
Quadratic twists by: -7 |