Atkin-Lehner |
2+ 3+ 7- 13- |
Signs for the Atkin-Lehner involutions |
Class |
122304cf |
Isogeny class |
Conductor |
122304 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
116736 |
Modular degree for the optimal curve |
Δ |
-3945037824 = -1 · 215 · 33 · 73 · 13 |
Discriminant |
Eigenvalues |
2+ 3+ 3 7- -3 13- -7 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1409,21057] |
[a1,a2,a3,a4,a6] |
Generators |
[19:28:1] |
Generators of the group modulo torsion |
j |
-27543608/351 |
j-invariant |
L |
6.719705402201 |
L(r)(E,1)/r! |
Ω |
1.3977905022397 |
Real period |
R |
1.2018441656171 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999445123 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122304ej1 61152bw1 122304dv1 |
Quadratic twists by: -4 8 -7 |