Atkin-Lehner |
2+ 3- 7+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
49728bs |
Isogeny class |
Conductor |
49728 |
Conductor |
∏ cp |
40 |
Product of Tamagawa factors cp |
deg |
430080 |
Modular degree for the optimal curve |
Δ |
-52179106416869376 = -1 · 214 · 38 · 7 · 375 |
Discriminant |
Eigenvalues |
2+ 3- 1 7+ 3 1 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-57365,12177267] |
[a1,a2,a3,a4,a6] |
Generators |
[-98:4107:1] |
Generators of the group modulo torsion |
j |
-1274243237085184/3184759913139 |
j-invariant |
L |
8.6153889297771 |
L(r)(E,1)/r! |
Ω |
0.31411902519376 |
Real period |
R |
0.68567869491981 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000004 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
49728dq1 3108a1 |
Quadratic twists by: -4 8 |