Atkin-Lehner |
2- 3+ 19+ 41- |
Signs for the Atkin-Lehner involutions |
Class |
37392j |
Isogeny class |
Conductor |
37392 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
338688 |
Modular degree for the optimal curve |
Δ |
-705199739613216768 = -1 · 219 · 314 · 193 · 41 |
Discriminant |
Eigenvalues |
2- 3+ -2 2 1 2 -4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-123984,-43716672] |
[a1,a2,a3,a4,a6] |
Generators |
[1016:29632:1] |
Generators of the group modulo torsion |
j |
-51459338321140177/172167905179008 |
j-invariant |
L |
4.2579840904273 |
L(r)(E,1)/r! |
Ω |
0.11703100911207 |
Real period |
R |
4.5479229423198 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999962 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4674i1 112176p1 |
Quadratic twists by: -4 -3 |