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feat: add formula for the j-invariant of an elliptic curve #41504

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feat: add formula for the j-invariant of an elliptic curve #41504

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92858b6
feat: discriminant formula
Paul-Lez Jul 8, 2026
0917c11
fix variable
Paul-Lez Jul 8, 2026
ce9a869
fix build
Paul-Lez Jul 8, 2026
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4 changes: 4 additions & 0 deletions Mathlib/AlgebraicGeometry/EllipticCurve/Weierstrass.lean
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Expand Up @@ -395,6 +395,10 @@ lemma j_eq_zero (h : W.c₄ = 0) : W.j = 0 := by
lemma j_eq_zero_iff [IsReduced R] : W.j = 0 ↔ W.c₄ = 0 := by
rw [j_eq_zero_iff', pow_eq_zero_iff three_ne_zero]

theorem j_eq {K : Type*} [Field K] (W : WeierstrassCurve K) [W.IsElliptic] :

@Multramate Multramate Jul 8, 2026

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Make this a lemma. Surely K and W are already defined elsewhere. Can you also move this up to right below the definition?

@Paul-Lez Paul-Lez Jul 9, 2026

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K and W are defined elsewhere (R instead of K, but as a CommRing so can't be used directly).

@Multramate Multramate Jul 9, 2026

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Ah gotcha, this is one of the few stupid files where we don't have W' for R and W for K...

W.j = W.Δ⁻¹ * W.c₄ ^ 3 := by
rw [WeierstrassCurve.j, Units.val_inv_eq_inv_val, WeierstrassCurve.coe_Δ']

section CharTwo

variable [CharP R 2]
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