Atkin-Lehner |
2+ 3+ 5+ 7+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
57120a |
Isogeny class |
Conductor |
57120 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
147456 |
Modular degree for the optimal curve |
Δ |
-69641775000000 = -1 · 26 · 34 · 58 · 7 · 173 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 7+ -2 0 17- -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,7714,302736] |
[a1,a2,a3,a4,a6] |
Generators |
[-25:306:1] [-2:536:1] |
Generators of the group modulo torsion |
j |
793097061902144/1088152734375 |
j-invariant |
L |
7.8517771240456 |
L(r)(E,1)/r! |
Ω |
0.41631169376694 |
Real period |
R |
3.1433888124386 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999992 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
57120s1 114240kd1 |
Quadratic twists by: -4 8 |