This works in 3.1.1:
sage: p=10^4+7; p
10007
sage: F.<i>=GF(p^2)
sage: E = EllipticCurve([0,0,0,i,i+3]); E
Elliptic Curve defined by y^2 = x^3 + i*x + (i+3) over Finite Field in i of size 10007^2
sage: E.abelian_group()
(Multiplicative Abelian Group isomorphic to C100130006,
((8287*i + 5423 : 9131*i + 6741 : 1),))
but this does not:
sage: K.<i> = QuadraticField(-1)
sage: P=K.factor(p)[0][0]; P
Fractional ideal (10007)
sage: E = EllipticCurve([0,0,0,i,i+3]); E
Elliptic Curve defined by y^2 = x^3 + i*x + (i+3) over Number Field in i with defining polynomial x^2 + 1
sage: Emod = E.change_ring(K.ring_of_integers().residue_field(P)); Emod
Elliptic Curve defined by y^2 = x^3 + ibar*x + (ibar+3) over Residue field in ibar of Fractional ideal (10007)
sage: Emod.abelian_group()
---------------------------------------------------------------------------
UnboundLocalError Traceback (most recent call last)
/home/john/sage-3.1.final/<ipython console> in <module>()
/home/john/sage-3.1.final/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_finite_field.py in abelian_group(self, debug)
1121 if debug: print "n1a=",n1a
1122 a = None
-> 1123 for m in (N//n1).divisors():
1124 try:
1125 a = generic.bsgs(m*P1a,m*Q,(0,(n1b//m)-1),operation='+')
UnboundLocalError: local variable 'N' referenced before assignment
That's a bug in code I wrote, and I will fix it. But it's a mystery why it only arises when the same (abstract) finite field is defined as a quotient field of ZZ[i].
