Atkin-Lehner |
2+ 3+ 11- 23- |
Signs for the Atkin-Lehner involutions |
Class |
12144f |
Isogeny class |
Conductor |
12144 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
2688 |
Modular degree for the optimal curve |
Δ |
-8852976 = -1 · 24 · 37 · 11 · 23 |
Discriminant |
Eigenvalues |
2+ 3+ -3 3 11- 2 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,28,-141] |
[a1,a2,a3,a4,a6] |
Generators |
[19:83:1] |
Generators of the group modulo torsion |
j |
146377472/553311 |
j-invariant |
L |
3.644031844258 |
L(r)(E,1)/r! |
Ω |
1.1760407299419 |
Real period |
R |
3.0985592177901 |
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 |
6072k1 48576dg1 36432g1 |
Quadratic twists by: -4 8 -3 |