Atkin-Lehner |
2+ 3- 5+ 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68970y |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
112 |
Product of Tamagawa factors cp |
deg |
716800 |
Modular degree for the optimal curve |
Δ |
-3219862110951420 = -1 · 22 · 314 · 5 · 116 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -2 11- -6 -4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-176179,28578746] |
[a1,a2,a3,a4,a6] |
Generators |
[109:-3322:1] |
Generators of the group modulo torsion |
j |
-341370886042369/1817528220 |
j-invariant |
L |
3.7026648351432 |
L(r)(E,1)/r! |
Ω |
0.45036972223844 |
Real period |
R |
0.29362104797618 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000465 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
570j1 |
Quadratic twists by: -11 |