Atkin-Lehner |
2- 11+ 13- 23- |
Signs for the Atkin-Lehner involutions |
Class |
6578d |
Isogeny class |
Conductor |
6578 |
Conductor |
∏ cp |
108 |
Product of Tamagawa factors cp |
deg |
22464 |
Modular degree for the optimal curve |
Δ |
-72001419776 = -1 · 29 · 112 · 133 · 232 |
Discriminant |
Eigenvalues |
2- -3 -3 -3 11+ 13- -7 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-2529,51249] |
[a1,a2,a3,a4,a6] |
Generators |
[-57:116:1] [-39:318:1] |
Generators of the group modulo torsion |
j |
-1788171617409633/72001419776 |
j-invariant |
L |
4.2010282955406 |
L(r)(E,1)/r! |
Ω |
1.0849401760719 |
Real period |
R |
0.035853046095798 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
52624i1 59202r1 72358c1 85514h1 |
Quadratic twists by: -4 -3 -11 13 |