Atkin-Lehner |
2- 3- 13+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
99216bb |
Isogeny class |
Conductor |
99216 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
1013760 |
Modular degree for the optimal curve |
Δ |
-153862130595004416 = -1 · 223 · 36 · 132 · 533 |
Discriminant |
Eigenvalues |
2- 3- 1 2 1 13+ -3 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1116387,454407138] |
[a1,a2,a3,a4,a6] |
Generators |
[-687:29952:1] |
Generators of the group modulo torsion |
j |
-51532421181502689/51528116224 |
j-invariant |
L |
8.2670826106545 |
L(r)(E,1)/r! |
Ω |
0.32294821626645 |
Real period |
R |
1.5999241846028 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000030712 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
12402b1 11024g1 |
Quadratic twists by: -4 -3 |