Atkin-Lehner |
2+ 3+ 5- 11- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
61710q |
Isogeny class |
Conductor |
61710 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
144000 |
Modular degree for the optimal curve |
Δ |
-159015315360 = -1 · 25 · 3 · 5 · 117 · 17 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -3 11- 0 17+ 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-19967,1077861] |
[a1,a2,a3,a4,a6] |
Generators |
[61:272:1] |
Generators of the group modulo torsion |
j |
-496981290961/89760 |
j-invariant |
L |
3.7976131341938 |
L(r)(E,1)/r! |
Ω |
0.99248308843781 |
Real period |
R |
0.95659391551943 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999988721 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5610bc1 |
Quadratic twists by: -11 |