Atkin-Lehner |
3+ 5- 11+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
8415f |
Isogeny class |
Conductor |
8415 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
5184 |
Modular degree for the optimal curve |
Δ |
-5318641845 = -1 · 39 · 5 · 11 · 173 |
Discriminant |
Eigenvalues |
1 3+ 5- 3 11+ -1 17+ -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-1419,21230] |
[a1,a2,a3,a4,a6] |
j |
-16060229667/270215 |
j-invariant |
L |
2.7220551861472 |
L(r)(E,1)/r! |
Ω |
1.3610275930736 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8415e1 42075g1 92565s1 |
Quadratic twists by: -3 5 -11 |