Theorems · Definition · algebraic geometry
WeierstrassCurve.ofJNe0Or1728
{R : Type u_1} → [CommRing R] → R → WeierstrassCurve RThe Weierstrass curve Y² + (j - 1728)XY = X³ - 36(j - 1728)³X - (j - 1728)⁵.
It is a modification of the curve in [silverman2009], Chapter III, Proposition 1.4 (c) to avoid
denominators. It is of j-invariant j if it is an elliptic curve.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext
- Assumes
- CommRing
Around this declaration
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Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- WeierstrassCurvestatement · cited by 394
Cited by7
Results whose statement or proof uses this declaration.
- WeierstrassCurve.ofJproof · cited by 8
- WeierstrassCurve.ofJNe0Or1728_c₄statement · cited by 1
- WeierstrassCurve.ofJNe0Or1728_jstatement and proof · cited by 1
- WeierstrassCurve.ofJNe0Or1728_Δstatement · cited by 1
- WeierstrassCurve.ofJ_1728_of_two_ne_zeroproof · cited by 1
- WeierstrassCurve.ofJ_ne_0_ne_1728statement and proof · cited by 1
- WeierstrassCurve.ofJ_jproof · cited by 0