The two literal arithmetic Picard descent endomorphisms have product nineteen
ProvedMazurTransfer.Order13ActualPicardCyclotomicNorm.pi_comp_piConjugate_nineteenalgebraic-geometryarithmetic-geometrymazur-theorem
For the actual arithmetic degree-zero Picard group of the order-thirteen curve over Q, the original endomorphisms pi=3+2rho and piConjugate=5-2rho satisfy pi*piConjugate=19 in the endomorphism ring. This is the complete original statement, with all literal constructors retained.
Preamble
import Definitions.Def_MazurTransfer_Order13ActualDiamondPicardEndomorphismsExplicitPublicOrderCertificate20261017
Formal statement
theorem MazurTransfer.Order13ActualPicardCyclotomicNorm.pi_comp_piConjugate_nineteen : MazurTransfer.Order13ActualDiamondPicardEndomorphisms.pi * MazurTransfer.Order13ActualDiamondPicardEndomorphisms.piConjugate = 19 := by sorry
Source
Complete original MazurTheorem Order13ActualPicardCyclotomicNorm.pi_comp_piConjugate_nineteen calculation; the square relation is derived from the accepted original cyclotomic identity. Official Anthropic FLT arithmetic Pic0 interfaces at 6e837e75355538c7f80bab5b956861e86c4eacc2, Apache-2.0.