Atkin-Lehner |
2+ 5- 11+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
56870h |
Isogeny class |
Conductor |
56870 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
120960 |
Modular degree for the optimal curve |
Δ |
-16014592000000 = -1 · 214 · 56 · 113 · 47 |
Discriminant |
Eigenvalues |
2+ 0 5- -3 11+ 1 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,5131,129333] |
[a1,a2,a3,a4,a6] |
Generators |
[47:-711:1] [122:1539:1] |
Generators of the group modulo torsion |
j |
11222874049869/12032000000 |
j-invariant |
L |
7.0812208931905 |
L(r)(E,1)/r! |
Ω |
0.46194805444866 |
Real period |
R |
0.63871006211241 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999998 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
56870u1 |
Quadratic twists by: -11 |