Atkin-Lehner |
3+ 5+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
8085j |
Isogeny class |
Conductor |
8085 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
288000 |
Modular degree for the optimal curve |
Δ |
-1998539751464746875 = -1 · 35 · 55 · 711 · 113 |
Discriminant |
Eigenvalues |
-2 3+ 5+ 7- 11- 6 7 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-438076,-130549434] |
[a1,a2,a3,a4,a6] |
Generators |
[810:6737:1] |
Generators of the group modulo torsion |
j |
-79028701534867456/16987307596875 |
j-invariant |
L |
1.9540898007023 |
L(r)(E,1)/r! |
Ω |
0.091731218898427 |
Real period |
R |
3.5503903399671 |
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 |
129360gd1 24255bo1 40425cs1 1155n1 |
Quadratic twists by: -4 -3 5 -7 |