Atkin-Lehner |
2+ 3+ 7+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
4872b |
Isogeny class |
Conductor |
4872 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
107520 |
Modular degree for the optimal curve |
Δ |
-1223536126557927168 = -1 · 28 · 35 · 714 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ 0 7+ 4 -6 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1095708,-444290220] |
[a1,a2,a3,a4,a6] |
Generators |
[468500761423484028367232762:-15009419973032445063516513952:262891167878186186452723] |
Generators of the group modulo torsion |
j |
-568288203127281250000/4779437994366903 |
j-invariant |
L |
3.1736067947963 |
L(r)(E,1)/r! |
Ω |
0.07374419244713 |
Real period |
R |
43.035345421561 |
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 |
9744e1 38976r1 14616j1 121800bo1 |
Quadratic twists by: -4 8 -3 5 |