Atkin-Lehner |
2- 3+ 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
49686cg |
Isogeny class |
Conductor |
49686 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
774144 |
Modular degree for the optimal curve |
Δ |
357185216579772672 = 28 · 33 · 77 · 137 |
Discriminant |
Eigenvalues |
2- 3+ -2 7- 4 13+ 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-468049,119653295] |
[a1,a2,a3,a4,a6] |
Generators |
[-203:14466:1] |
Generators of the group modulo torsion |
j |
19968681097/628992 |
j-invariant |
L |
6.9153775489132 |
L(r)(E,1)/r! |
Ω |
0.30100507457937 |
Real period |
R |
2.871786114623 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000007 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
7098bd1 3822d1 |
Quadratic twists by: -7 13 |