Atkin-Lehner |
3- 11- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
77319r |
Isogeny class |
Conductor |
77319 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
2488320 |
Modular degree for the optimal curve |
Δ |
3706627119274874421 = 312 · 117 · 713 |
Discriminant |
Eigenvalues |
-2 3- -1 5 11- -1 -5 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-490413,94305010] |
[a1,a2,a3,a4,a6] |
Generators |
[-308:14701:1] |
Generators of the group modulo torsion |
j |
10100107472896/2870088309 |
j-invariant |
L |
3.0985246819632 |
L(r)(E,1)/r! |
Ω |
0.23175158002988 |
Real period |
R |
1.6712532667647 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001099 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
25773h1 7029c1 |
Quadratic twists by: -3 -11 |