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Namespace PeriodPair 18 theorems

• Non-vanishing of the discriminant g₂³-27g₃² PeriodPair.discriminant_ne_zero 0 below · cited by 15 · depth 11
• Cyclic N-isogeny of lattice curves comes from index-N sublattice PeriodPair.exists_scale_lattice_subset_and_sublatticeIndex_eq_and_isAddCyclic_sublatticeQuotient 58 below · cited by 2 · depth 11
• Every complex elliptic curve is a lattice curve PeriodPair.exists_variableChange_smul_weierstrassCurve_eq 2 below · cited by 3 · depth 11
• Lifting a function-field map of complex tori to an entire function PeriodPair.exists_differentiable_toPoint_comp_eq_pointMapOfPushforward_toPoint 55 below · cited by 1 · depth 12
• Cyclic index-N sublattices come from primitive coset representatives PeriodPair.exists_mem_primCosetReps_and_jLattice_eq_of_isAddCyclic 0 below · cited by 1 · depth 12
• Dual homothety for a homomorphism of lattice curves PeriodPair.exists_scale_lattice_subset_and_sublatticeIndex_eq_natCard_ker 2 below · cited by 1 · depth 12
• Uniformisation: z ↦ (wp(z), wp'(z)/2) parametrises E_Λ(ℂ) PeriodPair.isUniformization_toPoint 1 below · cited by 11 · depth 12
• Lattice j-invariant of ℤτ+ℤ equals E₄³/Δ PeriodPair.jLattice_ofTau 1 below · cited by 1 · depth 12
• Surjectivity of the j-invariant of period pairs PeriodPair.jLattice_surjective 1 below · cited by 2 · depth 12
• A lattice is determined by g₂ and g₃ PeriodPair.lattice_eq_of_g2_eq_of_g3_eq 0 below · cited by 3 · depth 14
• Rational homomorphisms of lattice curves lift to z ↦ az PeriodPair.exists_forall_apply_toPoint_eq_toPoint_mul_of_mem_rationalHomSet 2 below · cited by 1 · depth 19
• Lattice multipliers give rational homomorphisms of Weierstrass curves PeriodPair.exists_mem_rationalHomSet_forall_apply_toPoint_eq_toPoint_mul 2 below · cited by 1 · depth 19
• Division values of wp are weight-two forms for Γ(N) PeriodPair.weierstrassP_torsion_modularForm_slash_tendsto_atImInfty 1 below · cited by 4 · depth 21
• Division values of wp as weight-two forms on Γ₁(M) PeriodPair.exists_gamma1_two_eq_weierstrassP_and_slash_and_qExpansion_coeff 2 below · cited by 11 · depth 25
• Lattice invariants of ℤτ+ℤ in terms of E₄, E₆ PeriodPair.g2_ofTau_and_g3_ofTau 0 below · cited by 1 · depth 25
• Scaling a period lattice by a root of unity PeriodPair.scale_lattice_eq_of_pow_four_eq_one_or_g2_eq_zero 1 below · cited by 1 · depth 26
• wp separates points up to sign modulo the lattice PeriodPair.sub_mem_lattice_or_add_mem_lattice_of_weierstrassP_eq 2 below · cited by 1 · depth 26
• Homogeneity of wp under scaling of the period pair PeriodPair.weierstrassP_scale 0 below · cited by 1 · depth 26