Atkin-Lehner |
2+ 3- 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
122304dy |
Isogeny class |
Conductor |
122304 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
-549716364288 = -1 · 210 · 33 · 76 · 132 |
Discriminant |
Eigenvalues |
2+ 3- -4 7- 2 13+ 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,915,-33741] |
[a1,a2,a3,a4,a6] |
Generators |
[30:147:1] |
Generators of the group modulo torsion |
j |
702464/4563 |
j-invariant |
L |
7.4971027425495 |
L(r)(E,1)/r! |
Ω |
0.4607669302597 |
Real period |
R |
1.355910157358 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000015451 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
122304fu1 15288ba1 2496g1 |
Quadratic twists by: -4 8 -7 |