Atkin-Lehner |
2- 3- 5+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
69600bp |
Isogeny class |
Conductor |
69600 |
Conductor |
∏ cp |
44 |
Product of Tamagawa factors cp |
deg |
709632 |
Modular degree for the optimal curve |
Δ |
-1643924160000000 = -1 · 212 · 311 · 57 · 29 |
Discriminant |
Eigenvalues |
2- 3- 5+ 4 3 -4 -4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-683133,217104363] |
[a1,a2,a3,a4,a6] |
Generators |
[453:900:1] |
Generators of the group modulo torsion |
j |
-550884013682176/25686315 |
j-invariant |
L |
9.8188564642773 |
L(r)(E,1)/r! |
Ω |
0.44616256891302 |
Real period |
R |
0.50016707872214 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000232 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69600e1 13920f1 |
Quadratic twists by: -4 5 |