Atkin-Lehner |
2+ 3+ 5- 11+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
12210f |
Isogeny class |
Conductor |
12210 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
9984 |
Modular degree for the optimal curve |
Δ |
80586000 = 24 · 32 · 53 · 112 · 37 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -2 11+ -6 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-852,9216] |
[a1,a2,a3,a4,a6] |
Generators |
[-33:69:1] [27:-96:1] |
Generators of the group modulo torsion |
j |
68523370149961/80586000 |
j-invariant |
L |
4.2546289514183 |
L(r)(E,1)/r! |
Ω |
1.9199318225943 |
Real period |
R |
0.36933854467716 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
97680cz1 36630bh1 61050cb1 |
Quadratic twists by: -4 -3 5 |