Atkin-Lehner |
3- 7+ 11+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
61677g |
Isogeny class |
Conductor |
61677 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
268416 |
Modular degree for the optimal curve |
Δ |
-34970859 = -1 · 36 · 72 · 11 · 89 |
Discriminant |
Eigenvalues |
-2 3- 3 7+ 11+ -3 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-122961,16595838] |
[a1,a2,a3,a4,a6] |
Generators |
[203:13:1] |
Generators of the group modulo torsion |
j |
-282031971470553088/47971 |
j-invariant |
L |
3.3301971336372 |
L(r)(E,1)/r! |
Ω |
1.1930572504501 |
Real period |
R |
0.69782844286436 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000957 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6853e1 |
Quadratic twists by: -3 |