Atkin-Lehner |
2+ 3+ 5+ 7+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
30450d |
Isogeny class |
Conductor |
30450 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
506880 |
Modular degree for the optimal curve |
Δ |
-48342420000000000 = -1 · 211 · 35 · 510 · 73 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 7+ -5 7 6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-257000,51144000] |
[a1,a2,a3,a4,a6] |
Generators |
[-185:9705:1] |
Generators of the group modulo torsion |
j |
-120144998550165121/3093914880000 |
j-invariant |
L |
3.4363417817021 |
L(r)(E,1)/r! |
Ω |
0.35669940988953 |
Real period |
R |
4.8168593589296 |
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 |
91350eg1 6090bb1 |
Quadratic twists by: -3 5 |