Atkin-Lehner |
3+ 5+ 19- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
17385d |
Isogeny class |
Conductor |
17385 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
4608 |
Modular degree for the optimal curve |
Δ |
8918505 = 34 · 5 · 192 · 61 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 0 -2 -4 -2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-521,4358] |
[a1,a2,a3,a4,a6] |
Generators |
[-6:88:1] [22:53:1] |
Generators of the group modulo torsion |
j |
15641881075729/8918505 |
j-invariant |
L |
3.8140671841395 |
L(r)(E,1)/r! |
Ω |
2.2865796113515 |
Real period |
R |
1.6680229130028 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
52155l1 86925k1 |
Quadratic twists by: -3 5 |