Atkin-Lehner |
2- 3+ 17- 37- |
Signs for the Atkin-Lehner involutions |
Class |
120768cr |
Isogeny class |
Conductor |
120768 |
Conductor |
∏ cp |
56 |
Product of Tamagawa factors cp |
deg |
3548160 |
Modular degree for the optimal curve |
Δ |
-7.3359532901592E+19 |
Discriminant |
Eigenvalues |
2- 3+ 0 -3 -6 -1 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-713473,-472646495] |
[a1,a2,a3,a4,a6] |
Generators |
[1173:17408:1] [1768:61557:1] |
Generators of the group modulo torsion |
j |
-153220553571282625/279844409567232 |
j-invariant |
L |
8.5451234381741 |
L(r)(E,1)/r! |
Ω |
0.077435070874585 |
Real period |
R |
1.9705733882001 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999992496 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
120768bm1 30192bg1 |
Quadratic twists by: -4 8 |