Atkin-Lehner |
2- 3+ 5- 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
69300s |
Isogeny class |
Conductor |
69300 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
414720 |
Modular degree for the optimal curve |
Δ |
-37131979500000000 = -1 · 28 · 39 · 59 · 73 · 11 |
Discriminant |
Eigenvalues |
2- 3+ 5- 7- 11+ 0 1 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,27000,9112500] |
[a1,a2,a3,a4,a6] |
j |
221184/3773 |
j-invariant |
L |
3.26457761419 |
L(r)(E,1)/r! |
Ω |
0.27204813616194 |
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 |
69300v1 69300m1 |
Quadratic twists by: -3 5 |