Atkin-Lehner |
3+ 7+ 11+ 73- |
Signs for the Atkin-Lehner involutions |
Class |
50589b |
Isogeny class |
Conductor |
50589 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
7680 |
Modular degree for the optimal curve |
Δ |
-11686059 = -1 · 33 · 72 · 112 · 73 |
Discriminant |
Eigenvalues |
0 3+ -1 7+ 11+ 0 3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-108,462] |
[a1,a2,a3,a4,a6] |
Generators |
[6:-6:1] [-62:227:8] |
Generators of the group modulo torsion |
j |
-5159780352/432817 |
j-invariant |
L |
7.5460744043661 |
L(r)(E,1)/r! |
Ω |
2.2156764019276 |
Real period |
R |
0.42572069627367 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
50589d1 |
Quadratic twists by: -3 |