Atkin-Lehner |
3- 5+ 7- 37- |
Signs for the Atkin-Lehner involutions |
Class |
58275z |
Isogeny class |
Conductor |
58275 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
580608 |
Modular degree for the optimal curve |
Δ |
-304927921142578125 = -1 · 39 · 513 · 73 · 37 |
Discriminant |
Eigenvalues |
1 3- 5+ 7- 3 -4 -1 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,166833,4192366] |
[a1,a2,a3,a4,a6] |
j |
45083805930071/26770078125 |
j-invariant |
L |
2.2442739933481 |
L(r)(E,1)/r! |
Ω |
0.18702283294404 |
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 |
19425k1 11655k1 |
Quadratic twists by: -3 5 |