Strange curve

of the form [p,a,b]

data:
[[5, 3, 2],
 [11, 1, 5],
 [13, 1, 6],
 [13, 7, 10],
 [13, 8, 10],
 [13, 9, 7],
 [19, 11, 18],
 [23, 19, 11],
 [31, 1, 16],
 [31, 30, 28],
 [43, 5, 29],
 [43, 12, 38],
 [43, 26, 7],
 [43, 33, 10],
 [43, 36, 14],
 [53, 29, 4],
 [61, 23, 43],
 [61, 38, 47],
 [61, 53, 59],
 [71, 10, 32]]

[[7, 0, 5],
 [19, 0, 10],
 [19, 0, 13],
 [19, 0, 15],
 [37, 0, 5],
 [37, 0, 13],
 [37, 0, 18],
 [37, 0, 19],
 [37, 0, 24],
 [37, 0, 32],
 [61, 0, 2],
 [61, 0, 6],
 [61, 0, 7],
 [61, 0, 18],
 [61, 0, 21],
 [61, 0, 40],
 [61, 0, 43],
 [61, 0, 54],
 [61, 0, 55],
 [61, 0, 59]]


code:
curves = []
for p in Primes()[:20]:
    for i in range(0,p):
        for j in range(0,p):
            try:
                if EllipticCurve(GF(p), [i, j]).order()==p:
                    curves.append([p,i,j])
            except:
                pass
anomalous_anot0_curves = []
for p,a,b in curves:
    E = EllipticCurve(GF(p),[a,b])
    El = EllipticCurve(Qp(p), [a,b])
    for P in E.points()[1:]:
        for Pl in El.lift_x(ZZ(P.xy()[0]), all=True):
            if GF(p)(Pl.xy()[1]) == P.xy()[1]:
                break
        x,y = (p*Pl).xy()
        if x.valuation()<-2 and a!=0:
            print(x.valuation(),y.valuation(),a,b)
            anomalous_anot0_curves += [[p,a,b]]
            break
anomalous_a0_curves = []
for p in Primes()[2:20]:
    for i in range(1,p):
        if EllipticCurve(GF(p), [0, i]).order()==p:
            anomalous_a0_curves += [[p,0,i]]