Atkin-Lehner |
2- 3+ 5- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
12240bi |
Isogeny class |
Conductor |
12240 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
-25568870400000 = -1 · 220 · 33 · 55 · 172 |
Discriminant |
Eigenvalues |
2- 3+ 5- 4 2 -6 17+ 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1227,-243846] |
[a1,a2,a3,a4,a6] |
Generators |
[103:850:1] |
Generators of the group modulo torsion |
j |
-1847284083/231200000 |
j-invariant |
L |
5.6482104115303 |
L(r)(E,1)/r! |
Ω |
0.29745369018352 |
Real period |
R |
0.9494268516295 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
1530j1 48960dm1 12240be1 61200du1 |
Quadratic twists by: -4 8 -3 5 |