Atkin-Lehner |
2- 3+ 31+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
123504t |
Isogeny class |
Conductor |
123504 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
456192 |
Modular degree for the optimal curve |
Δ |
-21544245370224 = -1 · 24 · 38 · 313 · 832 |
Discriminant |
Eigenvalues |
2- 3+ -1 5 0 0 -2 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-72046,-7422641] |
[a1,a2,a3,a4,a6] |
Generators |
[5249645:1075785867:125] |
Generators of the group modulo torsion |
j |
-2584874003121566464/1346515335639 |
j-invariant |
L |
6.8015723960798 |
L(r)(E,1)/r! |
Ω |
0.14569780826789 |
Real period |
R |
11.670684092678 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000033697 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
30876d1 |
Quadratic twists by: -4 |