Atkin-Lehner |
2+ 3- 7+ 103- |
Signs for the Atkin-Lehner involutions |
Class |
12978f |
Isogeny class |
Conductor |
12978 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
399360 |
Modular degree for the optimal curve |
Δ |
3367903499340742656 = 226 · 38 · 7 · 1033 |
Discriminant |
Eigenvalues |
2+ 3- 2 7+ 4 0 -8 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-1360476,-604023728] |
[a1,a2,a3,a4,a6] |
Generators |
[-45772:129491:64] |
Generators of the group modulo torsion |
j |
382004974093878023617/4619895060824064 |
j-invariant |
L |
3.9971566741191 |
L(r)(E,1)/r! |
Ω |
0.13989248844903 |
Real period |
R |
4.7621769146139 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
103824cb1 4326f1 90846bk1 |
Quadratic twists by: -4 -3 -7 |