Theorems · Definition · algebraic geometry
WeierstrassCurve.ofJ
{F : Type u_2} → [Field F] → F → [DecidableEq F] → WeierstrassCurve FFor any element j of a field F, there exists an elliptic curve over F
with j-invariant equal to j (see WeierstrassCurve.ofJ_j).
Its coefficients are given explicitly (see WeierstrassCurve.ofJ0, WeierstrassCurve.ofJ1728
and WeierstrassCurve.ofJNe0Or1728).
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Quot.sound
- Assumes
- FieldDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- WeierstrassCurvestatement · cited by 394
- WeierstrassCurve.ofJ0proof · cited by 8
- WeierstrassCurve.ofJ1728proof · cited by 7
- WeierstrassCurve.ofJNe0Or1728proof · cited by 6
Cited by8
Results whose statement or proof uses this declaration.
- WeierstrassCurve.ofJ_0_of_three_eq_zerostatement · cited by 1
- WeierstrassCurve.ofJ_0_of_three_ne_zerostatement · cited by 1
- WeierstrassCurve.ofJ_1728_of_three_eq_zerostatement · cited by 1
- WeierstrassCurve.ofJ_1728_of_two_ne_zerostatement · cited by 1
- WeierstrassCurve.ofJ_ne_0_ne_1728statement · cited by 1
- WeierstrassCurve.ofJ_0_of_two_eq_zerostatement · cited by 0
- WeierstrassCurve.ofJ_1728_of_two_eq_zerostatement · cited by 0
- WeierstrassCurve.ofJ_jstatement and proof · cited by 0