Atkin-Lehner |
2+ 7+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
53312i |
Isogeny class |
Conductor |
53312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1198080 |
Modular degree for the optimal curve |
Δ |
-718060257774927872 = -1 · 244 · 74 · 17 |
Discriminant |
Eigenvalues |
2+ -3 2 7+ 5 3 17+ 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-97804,42435568] |
[a1,a2,a3,a4,a6] |
Generators |
[-471526:7602176:1331] |
Generators of the group modulo torsion |
j |
-164384733177/1140850688 |
j-invariant |
L |
4.6266626280072 |
L(r)(E,1)/r! |
Ω |
0.24554125744961 |
Real period |
R |
4.7106774194209 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999803 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
53312bl1 1666c1 53312be1 |
Quadratic twists by: -4 8 -7 |