Atkin-Lehner |
3+ 5- 17+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
72675i |
Isogeny class |
Conductor |
72675 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
172800 |
Modular degree for the optimal curve |
Δ |
-42218497265625 = -1 · 39 · 58 · 172 · 19 |
Discriminant |
Eigenvalues |
-1 3+ 5- 2 -1 -6 17+ 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,5695,-266678] |
[a1,a2,a3,a4,a6] |
Generators |
[38:40:1] [55:431:1] |
Generators of the group modulo torsion |
j |
2657205/5491 |
j-invariant |
L |
7.0806085955451 |
L(r)(E,1)/r! |
Ω |
0.33468549331807 |
Real period |
R |
5.2890017172779 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998814 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72675m1 72675f1 |
Quadratic twists by: -3 5 |