Atkin-Lehner |
3+ 7- 13- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
8463d |
Isogeny class |
Conductor |
8463 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
15542054073 = 32 · 73 · 132 · 313 |
Discriminant |
Eigenvalues |
1 3+ 2 7- -2 13- 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-212894,37720263] |
[a1,a2,a3,a4,a6] |
Generators |
[254:209:1] |
Generators of the group modulo torsion |
j |
1067129596696048382953/15542054073 |
j-invariant |
L |
4.9884664130905 |
L(r)(E,1)/r! |
Ω |
0.88265636112123 |
Real period |
R |
1.8838839337028 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
25389n1 59241s1 110019f1 |
Quadratic twists by: -3 -7 13 |