Atkin-Lehner |
3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
61347bc |
Isogeny class |
Conductor |
61347 |
Conductor |
∏ cp |
28 |
Product of Tamagawa factors cp |
deg |
564480 |
Modular degree for the optimal curve |
Δ |
-215864373506067 = -1 · 37 · 112 · 138 |
Discriminant |
Eigenvalues |
2 3- 2 3 11- 13+ 0 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-200152,34406389] |
[a1,a2,a3,a4,a6] |
Generators |
[1306:19769:8] |
Generators of the group modulo torsion |
j |
-1518309117952/369603 |
j-invariant |
L |
19.765240841658 |
L(r)(E,1)/r! |
Ω |
0.547058260339 |
Real period |
R |
1.2903588334193 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000102 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61347bd1 4719k1 |
Quadratic twists by: -11 13 |