Atkin-Lehner |
2- 3- 7- 103- |
Signs for the Atkin-Lehner involutions |
Class |
12978z |
Isogeny class |
Conductor |
12978 |
Conductor |
∏ cp |
288 |
Product of Tamagawa factors cp |
deg |
317952 |
Modular degree for the optimal curve |
Δ |
-5983878933785088 = -1 · 29 · 39 · 78 · 103 |
Discriminant |
Eigenvalues |
2- 3- -4 7- -1 -2 -6 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-1478957,692658965] |
[a1,a2,a3,a4,a6] |
Generators |
[735:-1880:1] |
Generators of the group modulo torsion |
j |
-490752533497730377609/8208338729472 |
j-invariant |
L |
5.3138707729949 |
L(r)(E,1)/r! |
Ω |
0.39015443201052 |
Real period |
R |
0.047291376619586 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
103824br1 4326b1 90846di1 |
Quadratic twists by: -4 -3 -7 |