Atkin-Lehner |
3- 5+ 7+ 13- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
69615i |
Isogeny class |
Conductor |
69615 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
2211840 |
Modular degree for the optimal curve |
Δ |
-6.7684136036965E+20 |
Discriminant |
Eigenvalues |
1 3- 5+ 7+ 4 13- 17+ 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-977940,-1305634869] |
[a1,a2,a3,a4,a6] |
Generators |
[51015722346977514186676877562950:-502157311160173335415687807216547:35881790611972481286624872567] |
Generators of the group modulo torsion |
j |
-141883882518531666241/928451797489227375 |
j-invariant |
L |
6.9681126717206 |
L(r)(E,1)/r! |
Ω |
0.06759977277291 |
Real period |
R |
51.539468151217 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000004 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23205m1 |
Quadratic twists by: -3 |