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Wow, Thank you very much !

I am new with Sagemath. I just find out that Sagemath has Elliptic Curve Library and I curious to find out how to find order of an elliptic curve over Gaussian Integer.

p = 107927
G = ZZ[I]
J = G.ideal(p)
Q = G.quotient(J,'x')
a = Q(I)

A = (95385+100114*a)
B = (18724+61222*a)
E = EllipticCurve(Q,[A, B])
E

it will show : Elliptic Curve defined by y^2 = x^3 + (-7813I-12542)x + (-46705I+18724) over Quotient of Gaussian Integers in Number Field in I with defining polynomial x^2 + 1 with I = 1I by the ideal (107927)

E.cardinality() AttributeError: 'EllipticCurve_field_with_category' object has no attribute 'cardinality'

why it shows an error ? I found the group order is 11648283482 (using python and the program that I made from scratch)

`

Thank you !

how to define Ring of gaussian integers modulo n? modulo operation defined as :

def modGI(x,n): 
    import math
    E=(x*n.conjugate())/(n*n.conjugate())
    return x-complex(math.floor(E.real),math.floor(E.imag))*n

how to define Ring of gaussian integers modulo n? modulo operation define as :

def modGI(x,n): import math E=(x*n.conjugate())/(n*n.conjugate()) return x-complex(math.floor(E.real),math.floor(E.imag))*n