Atkin-Lehner |
2+ 11- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
4136a |
Isogeny class |
Conductor |
4136 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
768 |
Modular degree for the optimal curve |
Δ |
-529408 = -1 · 210 · 11 · 47 |
Discriminant |
Eigenvalues |
2+ 0 -4 -1 11- -7 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,13,30] |
[a1,a2,a3,a4,a6] |
Generators |
[-1:4:1] [2:8:1] |
Generators of the group modulo torsion |
j |
237276/517 |
j-invariant |
L |
3.7009161909796 |
L(r)(E,1)/r! |
Ω |
2.0319258074203 |
Real period |
R |
0.91069176282554 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999971 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8272a1 33088b1 37224n1 103400be1 |
Quadratic twists by: -4 8 -3 5 |