Atkin-Lehner |
2+ 3- 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
122304cy |
Isogeny class |
Conductor |
122304 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
193536 |
Modular degree for the optimal curve |
Δ |
-24475592546496 = -1 · 26 · 36 · 79 · 13 |
Discriminant |
Eigenvalues |
2+ 3- 1 7- 2 13+ 2 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,915,-237483] |
[a1,a2,a3,a4,a6] |
Generators |
[212:3087:1] |
Generators of the group modulo torsion |
j |
32768/9477 |
j-invariant |
L |
9.9172581837915 |
L(r)(E,1)/r! |
Ω |
0.31604335859248 |
Real period |
R |
2.6149519155331 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999520801 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122304ez1 1911a1 122304bt1 |
Quadratic twists by: -4 8 -7 |