Atkin-Lehner |
2+ 3- 17+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
30192g |
Isogeny class |
Conductor |
30192 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
50688 |
Modular degree for the optimal curve |
Δ |
-642808452096 = -1 · 210 · 36 · 17 · 373 |
Discriminant |
Eigenvalues |
2+ 3- -3 3 -5 -6 17+ 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1232,41604] |
[a1,a2,a3,a4,a6] |
Generators |
[-32:222:1] |
Generators of the group modulo torsion |
j |
-202119559492/627742629 |
j-invariant |
L |
5.1126703664025 |
L(r)(E,1)/r! |
Ω |
0.80062155290687 |
Real period |
R |
0.17738545855195 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
15096d1 120768ch1 90576k1 |
Quadratic twists by: -4 8 -3 |