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curve #2517

y2 + xy = x3 − 16956121x + 2366883701
a-invariants
[1, 0, 0, -16956121, 2366883701]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/2ℤ
conductor (N)
30030
discriminant (Δ)
309580507925165039062500
Faltings height
3.1971
naive height
61.5520
primes of bad reduction
2, 3, 5, 7, 11, 13
regulator
9.810336964750826692646418134680001539420
submitted by
Natanael Wildner Fraga
submitted at
last updated

Witness: 1 independent point log in to add more points →

Commentary

Exact computational full 2- and 3-torsion family at (p,q)=(-25,1); Velu quotient by rational order-3 subgroup. The mapped rank >=1 witness is non-torsion by the original exact 2-descent Kummer certificate and finite isogeny kernel. Conductor N=30030; local exponents {'2': 1, '3': 1, '5': 1, '7': 1, '11': 1, '13': 1}.

last edited by Natanael Wildner Fraga at · history

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