Atkin-Lehner |
2- 3+ 7+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
84084c |
Isogeny class |
Conductor |
84084 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
1108800 |
Modular degree for the optimal curve |
Δ |
46926412561972944 = 24 · 35 · 78 · 115 · 13 |
Discriminant |
Eigenvalues |
2- 3+ -3 7+ 11+ 13- 3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1029457,-401553746] |
[a1,a2,a3,a4,a6] |
Generators |
[-61578130934167482:33828220222309346:104440531313357] |
Generators of the group modulo torsion |
j |
1308110598258688/508760109 |
j-invariant |
L |
4.0002569021595 |
L(r)(E,1)/r! |
Ω |
0.14988480381515 |
Real period |
R |
26.688875725474 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
84084t1 |
Quadratic twists by: -7 |