Atkin-Lehner |
2+ 3+ 11+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
78144b |
Isogeny class |
Conductor |
78144 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
491520 |
Modular degree for the optimal curve |
Δ |
2482853948264448 = 212 · 35 · 113 · 374 |
Discriminant |
Eigenvalues |
2+ 3+ 0 -2 11+ -4 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-427593,107736201] |
[a1,a2,a3,a4,a6] |
Generators |
[355:744:1] |
Generators of the group modulo torsion |
j |
2110845954540952000/606165514713 |
j-invariant |
L |
3.8338472486941 |
L(r)(E,1)/r! |
Ω |
0.44759019622221 |
Real period |
R |
4.2827649953871 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999983732 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
78144bi1 39072q1 |
Quadratic twists by: -4 8 |