Atkin-Lehner |
3+ 7+ 73+ |
Signs for the Atkin-Lehner involutions |
Class |
111909b |
Isogeny class |
Conductor |
111909 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
211968 |
Modular degree for the optimal curve |
Δ |
75656415177 = 34 · 74 · 733 |
Discriminant |
Eigenvalues |
1 3+ -4 7+ 4 0 4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-3432,74835] |
[a1,a2,a3,a4,a6] |
Generators |
[-34:409:1] |
Generators of the group modulo torsion |
j |
11497268593/194481 |
j-invariant |
L |
5.2834821170238 |
L(r)(E,1)/r! |
Ω |
1.090559060931 |
Real period |
R |
2.4223732342171 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999204302 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
111909d1 |
Quadratic twists by: 73 |