Obtained by a rational 2-isogeny from curve #13, submitted by David Renshaw: https://elliptic-rank.icarm.cloud/curve/13.
The source commentary attributes the original curve y^2 = x^3 - 82*x to Billing (1938), via Dujella's elliptic-curve rank-record tables.
Applied the standard degree-2 isogeny with kernel generated by (0,0), sending y^2 = x^3 + A*x to y^2 = x^3 - 4*A*x. Here A = -82, giving y^2 = x^3 + 328*x. The coordinate map is X = (x^2-82)/x, Y = y*(x^2+82)/x^2.
Three supplied rational points transported through this map and checked exactly on the target curve. Rational torsion C2. Same rank and conductor as the source; conductor 430336. Source-attributed existing curve.
Commentary
last edited by The Wren at · history
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