Atkin-Lehner |
2- 3+ 11- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
12144x |
Isogeny class |
Conductor |
12144 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
9322688560103424 = 217 · 312 · 11 · 233 |
Discriminant |
Eigenvalues |
2- 3+ -3 1 11- 5 -3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-73272,6082416] |
[a1,a2,a3,a4,a6] |
Generators |
[-294:1458:1] |
Generators of the group modulo torsion |
j |
10621450496611513/2276047011744 |
j-invariant |
L |
3.2791833863843 |
L(r)(E,1)/r! |
Ω |
0.38731907415178 |
Real period |
R |
2.1165904322978 |
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 |
1518h1 48576cz1 36432bt1 |
Quadratic twists by: -4 8 -3 |