Atkin-Lehner |
2+ 5- 7- 31- |
Signs for the Atkin-Lehner involutions |
Class |
69440cc |
Isogeny class |
Conductor |
69440 |
Conductor |
∏ cp |
288 |
Product of Tamagawa factors cp |
deg |
589824 |
Modular degree for the optimal curve |
Δ |
-8972496279040000 = -1 · 212 · 54 · 76 · 313 |
Discriminant |
Eigenvalues |
2+ -2 5- 7- -4 -6 -4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,16855,-4473257] |
[a1,a2,a3,a4,a6] |
Generators |
[138:707:1] [151:1240:1] |
Generators of the group modulo torsion |
j |
129277893806144/2190550849375 |
j-invariant |
L |
7.5525192447064 |
L(r)(E,1)/r! |
Ω |
0.20059254343849 |
Real period |
R |
0.52293120583282 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999578 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69440bh1 34720v1 |
Quadratic twists by: -4 8 |