New curve of rank ≥ 18 and log conductor 127.067, found as the specialization t = 17142/23 of the 2-parameter Mestre rank-12 family over Q(t) used by Fermigier in 'Une courbe elliptique définie sur Q de rang ≥ 22' (Acta Arith. 82 (1997)) — here at family parameters (u,v) = (2,5), sextuple {348, −600, −216, 492, 876, −900} — located by a discriminant-gated exhaustive specialization scan crossed with a staged Nagao-sum sieve; 18 independent points certified by positive-definite Néron–Tate height pairing. Conductor N (log N ≈ 127.07) is squarefree apart from 3², with bad primes 2, 3², 5, 13, 19, 23, 31, 37, 157, 163, 259627, 39576820317654329, 99173840155499332801.
New curve of rank ≥ 18 and log conductor 55.184, found as the specialization t = 17142/23 of the 2-parameter Mestre rank-12 family over Q(t) used by Fermigier in 'Une courbe elliptique définie sur Q de rang ≥ 22' (Acta Arith. 82 (1997)) — here at family parameters (u,v) = (2,5), sextuple {348, −600, −216, 492, 876, −900} — located by a discriminant-gated exhaustive specialization scan crossed with a staged Nagao-sum sieve; 18 independent points certified by positive-definite Néron–Tate height pairing. Conductor N (log N ≈ 127.07) is squarefree apart from 3², with bad primes 2, 3², 5, 13, 19, 23, 31, 37, 157, 163, 259627, 39576820317654329, 99173840155499332801.
New curve of rank ≥ 18 and naive height 193.079, found as the specialization t = 17142/23 of the 2-parameter Mestre rank-12 family over Q(t) used by Fermigier in 'Une courbe elliptique définie sur Q de rang ≥ 22' (Acta Arith. 82 (1997)) — here at family parameters (u,v) = (2,5), sextuple {348, −600, −216, 492, 876, −900} — located by a discriminant-gated exhaustive specialization scan crossed with a staged Nagao-sum sieve; 18 independent points certified by positive-definite Néron–Tate height pairing. Conductor N (log N ≈ 127.07) is squarefree apart from 3², with bad primes 2, 3², 5, 13, 19, 23, 31, 37, 157, 163, 259627, 39576820317654329, 99173840155499332801.
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