Atkin-Lehner |
2+ 3- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
97344x |
Isogeny class |
Conductor |
97344 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
344064 |
Modular degree for the optimal curve |
Δ |
-1826819160910848 = -1 · 210 · 37 · 138 |
Discriminant |
Eigenvalues |
2+ 3- 0 0 -6 13+ -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-20280,2337608] |
[a1,a2,a3,a4,a6] |
Generators |
[-143:1521:1] [26:1352:1] |
Generators of the group modulo torsion |
j |
-256000/507 |
j-invariant |
L |
10.992939212715 |
L(r)(E,1)/r! |
Ω |
0.41831809818508 |
Real period |
R |
3.2848624231398 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999995775 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
97344eh1 12168b1 32448a1 7488v1 |
Quadratic twists by: -4 8 -3 13 |