#!/usr/bin/env sage

import sys
from sage.all import *

r = 21888242871839275222246405745257275088548364400416034343698204186575808495617
F = GF(r)
b = 7950939520449436327800262930799465135910802758673292356620796789196167463969
btwist = F(b)*125
print "b      =", b
print "btwist =", btwist

E = EllipticCurve(F, [-3, b])
print E
Ec = E.cardinality()
print "Ec  =", Ec
assert(Ec in Primes())

Et = EllipticCurve(F, [-75, btwist])
print Et
Etc = Et.cardinality()
print "Etc =", Etc
assert(Etc in Primes())
assert(Ec + Etc == 2*r+2)