Atkin-Lehner |
3+ 13- 17+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
45747a |
Isogeny class |
Conductor |
45747 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
9984 |
Modular degree for the optimal curve |
Δ |
-100048689 = -1 · 39 · 13 · 17 · 23 |
Discriminant |
Eigenvalues |
1 3+ -1 3 -2 13- 17+ 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-15,-478] |
[a1,a2,a3,a4,a6] |
Generators |
[1130:434:125] |
Generators of the group modulo torsion |
j |
-19683/5083 |
j-invariant |
L |
7.1742235077007 |
L(r)(E,1)/r! |
Ω |
0.84556286372419 |
Real period |
R |
4.2422768403669 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999968 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
45747b1 |
Quadratic twists by: -3 |