Atkin-Lehner |
3+ 7- 17+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
77469d |
Isogeny class |
Conductor |
77469 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
33223680 |
Modular degree for the optimal curve |
Δ |
271756594567825857 = 32 · 79 · 176 · 31 |
Discriminant |
Eigenvalues |
1 3+ -2 7- -4 2 17+ 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-5346974056,-150493124261381] |
[a1,a2,a3,a4,a6] |
Generators |
[1928067955164232083733742155163151885243010957951264040889281472151677623798337650:658957759941791633976627165071500419032541160239824809051655479998466703268632563157:12261931001877499079664195011851876006514394549549936295704207488145239828536] |
Generators of the group modulo torsion |
j |
418953268285959090408977071/6734381751 |
j-invariant |
L |
4.3020390150208 |
L(r)(E,1)/r! |
Ω |
0.017655195682238 |
Real period |
R |
121.83492872154 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
77469x1 |
Quadratic twists by: -7 |