Atkin-Lehner |
2- 3+ 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
122304fh |
Isogeny class |
Conductor |
122304 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
3096576 |
Modular degree for the optimal curve |
Δ |
232064877477888 = 214 · 33 · 79 · 13 |
Discriminant |
Eigenvalues |
2- 3+ 2 7- 4 13+ -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-7865937,-8488671183] |
[a1,a2,a3,a4,a6] |
Generators |
[-18364703827634762757828711716:6871912168875845806998745:11344366494356502085360064] |
Generators of the group modulo torsion |
j |
27923315228972368/120393 |
j-invariant |
L |
7.1843127918594 |
L(r)(E,1)/r! |
Ω |
0.090149211870901 |
Real period |
R |
39.84678680364 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999164673 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
122304di1 30576bd1 17472ct1 |
Quadratic twists by: -4 8 -7 |