Atkin-Lehner |
2+ 3- 5- 13+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
69030p |
Isogeny class |
Conductor |
69030 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
377856 |
Modular degree for the optimal curve |
Δ |
30193722000 = 24 · 39 · 53 · 13 · 59 |
Discriminant |
Eigenvalues |
2+ 3- 5- 0 4 13+ -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-485379,-130036347] |
[a1,a2,a3,a4,a6] |
Generators |
[1902:75369:1] |
Generators of the group modulo torsion |
j |
17347609394908926769/41418000 |
j-invariant |
L |
5.2935082870615 |
L(r)(E,1)/r! |
Ω |
0.18087530112626 |
Real period |
R |
4.8776774700864 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997533 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23010p1 |
Quadratic twists by: -3 |