Atkin-Lehner |
2+ 3- 5+ 17- 53- |
Signs for the Atkin-Lehner involutions |
Class |
27030d |
Isogeny class |
Conductor |
27030 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
510720 |
Modular degree for the optimal curve |
Δ |
-199508213760000000 = -1 · 220 · 3 · 57 · 172 · 532 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -2 6 -2 17- -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-302659,-67620418] |
[a1,a2,a3,a4,a6] |
j |
-3066072555969473727529/199508213760000000 |
j-invariant |
L |
1.8250471268403 |
L(r)(E,1)/r! |
Ω |
0.10139150704668 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
81090bi1 |
Quadratic twists by: -3 |