Atkin-Lehner |
2- 11- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
51304d |
Isogeny class |
Conductor |
51304 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-11633685189632 = -1 · 210 · 118 · 53 |
Discriminant |
Eigenvalues |
2- -1 0 -2 11- 3 -7 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-97808,-11742212] |
[a1,a2,a3,a4,a6] |
Generators |
[15822:1989724:1] |
Generators of the group modulo torsion |
j |
-57042062500/6413 |
j-invariant |
L |
3.3706741489034 |
L(r)(E,1)/r! |
Ω |
0.13498100738726 |
Real period |
R |
6.2428674488338 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999659 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
102608a1 4664a1 |
Quadratic twists by: -4 -11 |