Atkin-Lehner |
2- 3+ 7- 11- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
38346m |
Isogeny class |
Conductor |
38346 |
Conductor |
∏ cp |
270 |
Product of Tamagawa factors cp |
deg |
241920 |
Modular degree for the optimal curve |
Δ |
-8555764428288 = -1 · 29 · 32 · 75 · 113 · 83 |
Discriminant |
Eigenvalues |
2- 3+ -4 7- 11- -5 -7 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-27440,1743761] |
[a1,a2,a3,a4,a6] |
Generators |
[-187:709:1] [-33:-1601:1] |
Generators of the group modulo torsion |
j |
-2284951690355362561/8555764428288 |
j-invariant |
L |
9.1844059333869 |
L(r)(E,1)/r! |
Ω |
0.73767960953551 |
Real period |
R |
0.046112591200978 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999986 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
115038r1 |
Quadratic twists by: -3 |