Atkin-Lehner |
2+ 3+ 7+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
24024b |
Isogeny class |
Conductor |
24024 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-18760832842752 = -1 · 210 · 32 · 76 · 113 · 13 |
Discriminant |
Eigenvalues |
2+ 3+ 4 7+ 11- 13- 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,3024,-199332] |
[a1,a2,a3,a4,a6] |
Generators |
[117:1320:1] |
Generators of the group modulo torsion |
j |
2985557859644/18321125823 |
j-invariant |
L |
6.0264418635207 |
L(r)(E,1)/r! |
Ω |
0.34390539765344 |
Real period |
R |
2.9205909069959 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
48048ba1 72072bc1 |
Quadratic twists by: -4 -3 |