Atkin-Lehner |
2- 3- 5- 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
69300cm |
Isogeny class |
Conductor |
69300 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
1075200 |
Modular degree for the optimal curve |
Δ |
-1139392896468750000 = -1 · 24 · 316 · 59 · 7 · 112 |
Discriminant |
Eigenvalues |
2- 3- 5- 7- 11+ -6 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,226500,30265625] |
[a1,a2,a3,a4,a6] |
Generators |
[250:10125:1] |
Generators of the group modulo torsion |
j |
56409309184/50014503 |
j-invariant |
L |
5.4821743113172 |
L(r)(E,1)/r! |
Ω |
0.17895054189747 |
Real period |
R |
2.5529280566959 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002308 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23100q1 69300cg1 |
Quadratic twists by: -3 5 |