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When I use sage.rings.finite_rings.finite_field_ext_pari.FiniteField_ext_pari, I get different methods in the Class EllipticCurve and some I would like aren't there (like random_point). Any recommendations on how to handle this other than (attempting to) write these myself?

When I use sage.rings.finite_rings.finite_field_ext_pari.FiniteField_ext_pari

Thanks DSM. I no longer get the overflow. For what it's worth the K283 curve seems to work and the only real differences are the a and b invariants:

def K283_test():
  order = 2**283
  a = 0
  b = 1
  K.<x>= GF(2)[]
  K.<a> = GF(order=order, name='a', modulus=x^283 + x^12 + x^7 + x^5 + 1  )
  K283_curve = EllipticCurve(K, [1,a,0,0,b])

no overflow... I think it's related to the b parameter.

I'm new to Sage so forgive me if this is simple. I am trying to define the NIST B-283 elliptic curve as follows:

def B283_test():
  order = 2**283
  a = 1
  b = 0x027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5
  K.<x>= GF(2)[]
  K.<a> = GF(order=order, name='a', modulus=x^283 + x^12 + x^7 + x^5 + 1 )
  B283_curve = EllipticCurve(K, [1,a,0,0,b])

I get a fairly long traceback after the last line followed by:

OverflowError: long int too large to convert to int

Any help is appreciated.