Atkin-Lehner |
3+ 5- 11- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
8415j |
Isogeny class |
Conductor |
8415 |
Conductor |
∏ cp |
154 |
Product of Tamagawa factors cp |
deg |
221760 |
Modular degree for the optimal curve |
Δ |
-436748607861328125 = -1 · 33 · 511 · 117 · 17 |
Discriminant |
Eigenvalues |
-1 3+ 5- -3 11- -5 17+ -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-4703822,3927974546] |
[a1,a2,a3,a4,a6] |
Generators |
[1266:274:1] |
Generators of the group modulo torsion |
j |
-426297217929651309023523/16175874365234375 |
j-invariant |
L |
2.3548207503747 |
L(r)(E,1)/r! |
Ω |
0.27878906553925 |
Real period |
R |
0.054848075924445 |
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 |
8415b1 42075l1 92565q1 |
Quadratic twists by: -3 5 -11 |