Atkin-Lehner |
2+ 3- 11- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
78144bi |
Isogeny class |
Conductor |
78144 |
Conductor |
∏ cp |
120 |
Product of Tamagawa factors cp |
deg |
491520 |
Modular degree for the optimal curve |
Δ |
2482853948264448 = 212 · 35 · 113 · 374 |
Discriminant |
Eigenvalues |
2+ 3- 0 2 11- -4 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-427593,-107736201] |
[a1,a2,a3,a4,a6] |
Generators |
[-375:132:1] |
Generators of the group modulo torsion |
j |
2110845954540952000/606165514713 |
j-invariant |
L |
8.2945603888026 |
L(r)(E,1)/r! |
Ω |
0.18670214501919 |
Real period |
R |
1.4808900361096 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000514 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
78144b1 39072a1 |
Quadratic twists by: -4 8 |