Atkin-Lehner |
2+ 3+ 13+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
72384g |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
Δ |
-8170496675807232 = -1 · 233 · 3 · 13 · 293 |
Discriminant |
Eigenvalues |
2+ 3+ 0 -4 -3 13+ -3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-56993,-6788319] |
[a1,a2,a3,a4,a6] |
Generators |
[2425:118784:1] [1120:36511:1] |
Generators of the group modulo torsion |
j |
-78100886643625/31167971328 |
j-invariant |
L |
7.5849266713785 |
L(r)(E,1)/r! |
Ω |
0.15151190378256 |
Real period |
R |
4.1717990919265 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999797 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72384cx2 2262g2 |
Quadratic twists by: -4 8 |