Atkin-Lehner |
2+ 3- 7+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
51744z |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
60 |
Product of Tamagawa factors cp |
deg |
725760 |
Modular degree for the optimal curve |
Δ |
-694282009817088 = -1 · 212 · 35 · 78 · 112 |
Discriminant |
Eigenvalues |
2+ 3- -2 7+ 11+ -5 -4 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1332669,591707115] |
[a1,a2,a3,a4,a6] |
Generators |
[-915:32340:1] [702:1617:1] |
Generators of the group modulo torsion |
j |
-11085279718912/29403 |
j-invariant |
L |
10.072857521476 |
L(r)(E,1)/r! |
Ω |
0.44162891285046 |
Real period |
R |
0.38014032552275 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51744bw1 103488g1 51744h1 |
Quadratic twists by: -4 8 -7 |