Atkin-Lehner |
2- 3- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
2412b |
Isogeny class |
Conductor |
2412 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
432 |
Modular degree for the optimal curve |
Δ |
-12503808 = -1 · 28 · 36 · 67 |
Discriminant |
Eigenvalues |
2- 3- -2 2 4 -6 -3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,24,164] |
[a1,a2,a3,a4,a6] |
Generators |
[4:18:1] |
Generators of the group modulo torsion |
j |
8192/67 |
j-invariant |
L |
3.015498757972 |
L(r)(E,1)/r! |
Ω |
1.6438258324046 |
Real period |
R |
0.30573988826631 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9648s1 38592bd1 268a1 60300j1 |
Quadratic twists by: -4 8 -3 5 |