Atkin-Lehner |
3+ 7+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
399a |
Isogeny class |
Conductor |
399 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
120 |
Modular degree for the optimal curve |
Δ |
543185433 = 35 · 76 · 19 |
Discriminant |
Eigenvalues |
1 3+ 0 7+ -2 -4 -4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-210,-441] |
[a1,a2,a3,a4,a6] |
Generators |
[-10:33:1] |
Generators of the group modulo torsion |
j |
1031831907625/543185433 |
j-invariant |
L |
1.8881722279102 |
L(r)(E,1)/r! |
Ω |
1.3293482923248 |
Real period |
R |
2.8407487169643 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6384be1 25536bg1 1197d1 9975p1 |
Quadratic twists by: -4 8 -3 5 |