Atkin-Lehner |
2+ 3+ 5- 13- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
69030d |
Isogeny class |
Conductor |
69030 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
1622016 |
Modular degree for the optimal curve |
Δ |
-246629664409190400 = -1 · 216 · 39 · 52 · 133 · 592 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -2 4 13- 6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-678444,-216242992] |
[a1,a2,a3,a4,a6] |
Generators |
[4219:266230:1] |
Generators of the group modulo torsion |
j |
-1754586557622582867/12530085068800 |
j-invariant |
L |
5.0844607488224 |
L(r)(E,1)/r! |
Ω |
0.083139187621366 |
Real period |
R |
5.0963339262925 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999981757 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69030bb1 |
Quadratic twists by: -3 |