Atkin-Lehner |
2+ 29- 41- |
Signs for the Atkin-Lehner involutions |
Class |
68962f |
Isogeny class |
Conductor |
68962 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
91728 |
Modular degree for the optimal curve |
Δ |
-8191582208 = -1 · 213 · 293 · 41 |
Discriminant |
Eigenvalues |
2+ 1 -2 1 -3 -5 6 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-12662,547336] |
[a1,a2,a3,a4,a6] |
Generators |
[70:37:1] |
Generators of the group modulo torsion |
j |
-9204227407493/335872 |
j-invariant |
L |
3.513537062278 |
L(r)(E,1)/r! |
Ω |
1.2267580905883 |
Real period |
R |
1.4320415282745 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001536 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68962m1 |
Quadratic twists by: 29 |