I have found two elliptic curves over a number field whose reductions are isomorphic to supersingular elliptic curves (used Deuring Lifting Theorem). How can I check which reduction is isomorphic to which supersingular elliptic curve?
sage: H = hilbert_class_polynomial(-64)
sage: S = H.splitting_field(l)
sage: R = H.roots(ring = S)
sage: for r in R:
....: j0 = r[0]
....: E = EllipticCurve(j=j0)
....: I = S.ideal(p)
....: Ebar = E.reduction(I)
....: Ebar
....: Ebar.j_invariant()
Elliptic Curve defined by y^2 = x^3 + (67*lbar+26)*x + (54*lbar+71) over Residue field in lbar of Fractional ideal (179)
lbar
Elliptic Curve defined by y^2 = x^3 + (112*lbar+44)*x + (125*lbar+171) over Residue field in lbar of Fractional ideal (179)
178*lbar + 35
sage: p = 179
sage: F.<i> = GF(p^2, modulus=x^2+1)
sage: Rp = H.roots(ring=F)
sage: for r in Rp:
....: j0 = r[0]
....: EllipticCurve(j=j0)
....: j0
Elliptic Curve defined by y^2 = x^3 + (10*i+35)*x + (155*i+121) over Finite Field in i of size 179^2
99*i + 107
Elliptic Curve defined by y^2 = x^3 + (169*i+35)*x + (24*i+121) over Finite Field in i of size 179^2
80*i + 107
