Atkin-Lehner |
2+ 3- 7+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
72072m |
Isogeny class |
Conductor |
72072 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
70656 |
Modular degree for the optimal curve |
Δ |
-248644940544 = -1 · 28 · 36 · 7 · 114 · 13 |
Discriminant |
Eigenvalues |
2+ 3- -1 7+ 11- 13- 2 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,1572,-236] |
[a1,a2,a3,a4,a6] |
Generators |
[2:54:1] [20:-198:1] |
Generators of the group modulo torsion |
j |
2302045184/1332331 |
j-invariant |
L |
10.099203746508 |
L(r)(E,1)/r! |
Ω |
0.58813530257688 |
Real period |
R |
0.53661141526055 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999338 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8008c1 |
Quadratic twists by: -3 |