Atkin-Lehner |
3- 13- 23+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
83421p |
Isogeny class |
Conductor |
83421 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1037184 |
Modular degree for the optimal curve |
Δ |
-155413323 = -1 · 36 · 13 · 232 · 31 |
Discriminant |
Eigenvalues |
-2 3- -2 2 -3 13- 6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-2415351,-1444835790] |
[a1,a2,a3,a4,a6] |
Generators |
[1505170:163716548:125] |
Generators of the group modulo torsion |
j |
-2137651670366357966848/213187 |
j-invariant |
L |
2.4270205494663 |
L(r)(E,1)/r! |
Ω |
0.060551442841024 |
Real period |
R |
10.020490131552 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000031757 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9269e1 |
Quadratic twists by: -3 |