Atkin-Lehner |
2+ 3+ 5- 7- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
52290h |
Isogeny class |
Conductor |
52290 |
Conductor |
∏ cp |
288 |
Product of Tamagawa factors cp |
deg |
884736 |
Modular degree for the optimal curve |
Δ |
4119553265625000000 = 26 · 33 · 512 · 76 · 83 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 7- 0 -4 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-485304,86128128] |
[a1,a2,a3,a4,a6] |
Generators |
[-653:11474:1] |
Generators of the group modulo torsion |
j |
468168364742287902363/152576046875000000 |
j-invariant |
L |
4.7258401080575 |
L(r)(E,1)/r! |
Ω |
0.22773758157414 |
Real period |
R |
2.593906589426 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000035 |
(Analytic) order of Ш |
t |
6 |
Number of elements in the torsion subgroup |
Twists |
52290bq3 |
Quadratic twists by: -3 |