Atkin-Lehner |
2+ 3+ 5- 11- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
51150q |
Isogeny class |
Conductor |
51150 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
691200 |
Modular degree for the optimal curve |
Δ |
26737128000000000 = 212 · 34 · 59 · 113 · 31 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 4 11- -4 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-131450,16516500] |
[a1,a2,a3,a4,a6] |
Generators |
[385:4620:1] |
Generators of the group modulo torsion |
j |
128611737881333/13689409536 |
j-invariant |
L |
4.3846432106831 |
L(r)(E,1)/r! |
Ω |
0.36414240172675 |
Real period |
R |
2.0068354165213 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000066 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
51150cu1 |
Quadratic twists by: 5 |