Atkin-Lehner |
3- 11- 17- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
72369m |
Isogeny class |
Conductor |
72369 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
953856 |
Modular degree for the optimal curve |
Δ |
-5370196181822258193 = -1 · 315 · 116 · 173 · 43 |
Discriminant |
Eigenvalues |
-1 3- -2 0 11- -5 17- 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-378086,143055902] |
[a1,a2,a3,a4,a6] |
Generators |
[8268:745642:1] [249:-8144:1] |
Generators of the group modulo torsion |
j |
-8199113454190195993/7366524254900217 |
j-invariant |
L |
5.9664823982789 |
L(r)(E,1)/r! |
Ω |
0.22061033768129 |
Real period |
R |
0.37562977310044 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000045 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
24123c1 |
Quadratic twists by: -3 |