Atkin-Lehner |
2+ 3+ 13- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
77376j |
Isogeny class |
Conductor |
77376 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
-233051004066816 = -1 · 210 · 32 · 138 · 31 |
Discriminant |
Eigenvalues |
2+ 3+ -3 1 0 13- 0 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,14703,257049] |
[a1,a2,a3,a4,a6] |
Generators |
[0:507:1] [104:1703:1] |
Generators of the group modulo torsion |
j |
343251219630848/227588871159 |
j-invariant |
L |
8.1293657462886 |
L(r)(E,1)/r! |
Ω |
0.34972117324452 |
Real period |
R |
1.4528298484922 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000073 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
77376bt1 9672d1 |
Quadratic twists by: -4 8 |