Atkin-Lehner |
2+ 3+ 5+ 11+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
67650c |
Isogeny class |
Conductor |
67650 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1492992 |
Modular degree for the optimal curve |
Δ |
1490773413888000000 = 218 · 39 · 56 · 11 · 412 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 2 11+ 6 -2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-287700,8658000] |
[a1,a2,a3,a4,a6] |
Generators |
[-303201:5635412:729] |
Generators of the group modulo torsion |
j |
168548786637666625/95409498488832 |
j-invariant |
L |
4.224955300756 |
L(r)(E,1)/r! |
Ω |
0.23122786133124 |
Real period |
R |
9.135913113311 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999994276 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
2706o1 |
Quadratic twists by: 5 |