Atkin-Lehner |
2+ 3+ 5- 41- |
Signs for the Atkin-Lehner involutions |
Class |
3690c |
Isogeny class |
Conductor |
3690 |
Conductor |
∏ cp |
22 |
Product of Tamagawa factors cp |
deg |
22176 |
Modular degree for the optimal curve |
Δ |
-315235546875000 = -1 · 23 · 39 · 511 · 41 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -5 0 4 2 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-22479,1558853] |
[a1,a2,a3,a4,a6] |
Generators |
[-83:1729:1] |
Generators of the group modulo torsion |
j |
-63822564229347/16015625000 |
j-invariant |
L |
2.4786770897069 |
L(r)(E,1)/r! |
Ω |
0.51770047139267 |
Real period |
R |
0.21762997460314 |
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 |
29520bg1 118080j1 3690m1 18450bf1 |
Quadratic twists by: -4 8 -3 5 |