Atkin-Lehner |
2- 3+ 13+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
72384bv |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
1575936 |
Modular degree for the optimal curve |
Δ |
-236429497149161472 = -1 · 237 · 33 · 133 · 29 |
Discriminant |
Eigenvalues |
2- 3+ 2 2 3 13+ 5 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-3329217,-2337097887] |
[a1,a2,a3,a4,a6] |
Generators |
[8448631998960899369987376476512066863872971:1413836904370624224025179243623713836414084044:300377740723629049453848097826750913521] |
Generators of the group modulo torsion |
j |
-15567190192349720497/901906956288 |
j-invariant |
L |
7.6731751951973 |
L(r)(E,1)/r! |
Ω |
0.055883360299269 |
Real period |
R |
68.653487854932 |
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 |
72384bd1 18096bf1 |
Quadratic twists by: -4 8 |