Atkin-Lehner |
2+ 3+ 5+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
44400c |
Isogeny class |
Conductor |
44400 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
608256 |
Modular degree for the optimal curve |
Δ |
-975585937500000000 = -1 · 28 · 33 · 518 · 37 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 0 0 -6 -2 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-512508,-148831488] |
[a1,a2,a3,a4,a6] |
Generators |
[221181684734140:-36353746238329976:8181353375] |
Generators of the group modulo torsion |
j |
-3721915550952016/243896484375 |
j-invariant |
L |
4.3984493281579 |
L(r)(E,1)/r! |
Ω |
0.088879885682151 |
Real period |
R |
24.743783671608 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000012 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
22200g1 8880i1 |
Quadratic twists by: -4 5 |