Atkin-Lehner |
2+ 3- 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
61152t |
Isogeny class |
Conductor |
61152 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
331776 |
Modular degree for the optimal curve |
Δ |
-5402612428222464 = -1 · 212 · 36 · 77 · 133 |
Discriminant |
Eigenvalues |
2+ 3- 3 7- 4 13+ -4 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-19469,3681243] |
[a1,a2,a3,a4,a6] |
Generators |
[121:1764:1] |
Generators of the group modulo torsion |
j |
-1693669888/11211291 |
j-invariant |
L |
10.286634609497 |
L(r)(E,1)/r! |
Ω |
0.36947762884686 |
Real period |
R |
0.58002128131382 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998743 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61152f1 122304gm1 8736e1 |
Quadratic twists by: -4 8 -7 |