Atkin-Lehner |
3+ 5+ 13- 43- |
Signs for the Atkin-Lehner involutions |
Class |
8385c |
Isogeny class |
Conductor |
8385 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
9600 |
Modular degree for the optimal curve |
Δ |
-29999978775 = -1 · 33 · 52 · 13 · 434 |
Discriminant |
Eigenvalues |
1 3+ 5+ -4 -4 13- -6 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-433,8848] |
[a1,a2,a3,a4,a6] |
Generators |
[144:1648:1] |
Generators of the group modulo torsion |
j |
-9010598335129/29999978775 |
j-invariant |
L |
2.9261965642657 |
L(r)(E,1)/r! |
Ω |
1.0315079723461 |
Real period |
R |
1.4184071489095 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
25155o1 41925i1 109005h1 |
Quadratic twists by: -3 5 13 |