Atkin-Lehner |
2- 3+ 5+ 13- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
69030z |
Isogeny class |
Conductor |
69030 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
1751040 |
Modular degree for the optimal curve |
Δ |
-79374802312166400 = -1 · 210 · 39 · 52 · 13 · 594 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 4 0 13- -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-5012633,4320908281] |
[a1,a2,a3,a4,a6] |
Generators |
[1303:-4:1] |
Generators of the group modulo torsion |
j |
-707668826813696578923/4032657740800 |
j-invariant |
L |
11.225531211633 |
L(r)(E,1)/r! |
Ω |
0.30483821559913 |
Real period |
R |
1.8412276803032 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000112 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69030f1 |
Quadratic twists by: -3 |