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You can probably adapt this code: {{{ sage: E=EllipticCurve([1,2,3,4,5]) sage: K=Qp(7) sage: f,h=E.hyperelliptic_polynomials() sage: n=3 sage: xvals=E.division_polynomial(n).roots(K,multiplicities=false) sage: [(x1,y1) for x1 in xvals for y1 in KX([-f(x1),h(x1),1]).roots(multiplicities=false)] [(37 + 57^2 + 57^3 + 57^4 + 47^5 + 47^6 + 27^7 + 57^8 + 27^9 + 67^10 + 27^12 + 57^13 + 37^14 + 7^15 + 67^17 + 27^18 + 47^19 + O(7^20), 6 + 7 + 27^3 + 27^4 + 47^5 + 57^7 + 37^8 + 27^9 + 37^10 + 47^11 + 57^12 + 37^13 + 27^14 + 37^15 + 67^16 + 47^17 + 67^18 + 47^19 + O(7^20)), (37 + 57^2 + 57^3 + 57^4 + 47^5 + 47^6 + 27^7 + 57^8 + 27^9 + 67^10 + 27^12 + 57^13 + 37^14 + 7^15 + 67^17 + 27^18 + 47^19 + O(7^20), 5 + 7 + 7^2 + 67^3 + 57^4 + 47^5 + 7^6 + 67^7 + 47^8 + 7^9 + 47^10 + 7^11 + 67^12 + 47^13 + 27^15 + 37^17 + 47^18 + 47^19 + O(7^20))] }}}

You can probably adapt this ~~code: {{{~~ code:

sage: E=EllipticCurve([1,2,3,4,5])
sage: K=Qp(7)
sage: f,h=E.hyperelliptic_polynomials()
sage: n=3
sage: xvals=E.division_polynomial(n).roots(K,multiplicities=false)
sage: [(x1,y1) for x1 in xvals for y1 in KX([-f(x1),h(x1),1]).roots(multiplicities=false)]
[(37 [(3*7 + 57^2 5*7^2 + 57^3 5*7^3 + 57^4 5*7^4 + 47^5 4*7^5 + 47^6 4*7^6 + 27^7 2*7^7 + 57^8 5*7^8 + 27^9 2*7^9 + 67^10 6*7^10 + 27^12 2*7^12 + 57^13 5*7^13 + 37^14 3*7^14 + 7^15 + 67^17 6*7^17 + 27^18 2*7^18 + 47^19 4*7^19 + O(7^20),
  6 + 7 + 27^3 2*7^3 + 27^4 2*7^4 + 47^5 4*7^5 + 57^7 5*7^7 + 37^8 3*7^8 + 27^9 2*7^9 + 37^10 3*7^10 + 47^11 4*7^11 + 57^12 5*7^12 + 37^13 3*7^13 + 27^14 2*7^14 + 37^15 3*7^15 + 67^16 6*7^16 + 47^17 4*7^17 + 67^18 6*7^18 + 47^19 4*7^19 + O(7^20)),
 (37 (3*7 + 57^2 5*7^2 + 57^3 5*7^3 + 57^4 5*7^4 + 47^5 4*7^5 + 47^6 4*7^6 + 27^7 2*7^7 + 57^8 5*7^8 + 27^9 2*7^9 + 67^10 6*7^10 + 27^12 2*7^12 + 57^13 5*7^13 + 37^14 3*7^14 + 7^15 + 67^17 6*7^17 + 27^18 2*7^18 + 47^19 4*7^19 + O(7^20),
  5 + 7 + 7^2 + 67^3 6*7^3 + 57^4 5*7^4 + 47^5 4*7^5 + 7^6 + 67^7 6*7^7 + 47^8 4*7^8 + 7^9 + 47^10 4*7^10 + 7^11 + 67^12 6*7^12 + 47^13 4*7^13 + 27^15 2*7^15 + 37^17 3*7^17 + 47^18 4*7^18 + 47^19 4*7^19 + O(7^20))]
}}}

You can probably adapt this code:

sage: E=EllipticCurve([1,2,3,4,5])
sage: K=Qp(7)
sage: KX=K['X']
sage: f,h=E.hyperelliptic_polynomials()
sage: n=3
sage: xvals=E.division_polynomial(n).roots(K,multiplicities=false)
sage: [(x1,y1) for x1 in xvals for y1 in KX([-f(x1),h(x1),1]).roots(multiplicities=false)]
[(3*7 + 5*7^2 + 5*7^3 + 5*7^4 + 4*7^5 + 4*7^6 + 2*7^7 + 5*7^8 + 2*7^9 + 6*7^10 + 2*7^12 + 5*7^13 + 3*7^14 + 7^15 + 6*7^17 + 2*7^18 + 4*7^19 + O(7^20),
  6 + 7 + 2*7^3 + 2*7^4 + 4*7^5 + 5*7^7 + 3*7^8 + 2*7^9 + 3*7^10 + 4*7^11 + 5*7^12 + 3*7^13 + 2*7^14 + 3*7^15 + 6*7^16 + 4*7^17 + 6*7^18 + 4*7^19 + O(7^20)),
 (3*7 + 5*7^2 + 5*7^3 + 5*7^4 + 4*7^5 + 4*7^6 + 2*7^7 + 5*7^8 + 2*7^9 + 6*7^10 + 2*7^12 + 5*7^13 + 3*7^14 + 7^15 + 6*7^17 + 2*7^18 + 4*7^19 + O(7^20),
  5 + 7 + 7^2 + 6*7^3 + 5*7^4 + 4*7^5 + 7^6 + 6*7^7 + 4*7^8 + 7^9 + 4*7^10 + 7^11 + 6*7^12 + 4*7^13 + 2*7^15 + 3*7^17 + 4*7^18 + 4*7^19 + O(7^20))]

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