Atkin-Lehner |
2+ 3- 11- 43- |
Signs for the Atkin-Lehner involutions |
Class |
68112x |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
168 |
Product of Tamagawa factors cp |
deg |
1698816 |
Modular degree for the optimal curve |
Δ |
-3469787694870875136 = -1 · 210 · 37 · 117 · 433 |
Discriminant |
Eigenvalues |
2+ 3- -3 -5 11- 0 -7 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-147819,92251946] |
[a1,a2,a3,a4,a6] |
Generators |
[163:8514:1] [-431:8712:1] |
Generators of the group modulo torsion |
j |
-478505580437668/4648099514091 |
j-invariant |
L |
7.3582039996745 |
L(r)(E,1)/r! |
Ω |
0.21365937641271 |
Real period |
R |
0.20499373379673 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999712 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34056e1 22704f1 |
Quadratic twists by: -4 -3 |