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curve #2531

y2 + xy = x3 − x2 − 4898934x − 4172120460
a-invariants
[1, -1, 0, -4898934, -4172120460]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/2ℤ
conductor (N)
10710
discriminant (Δ)
561793182180249600
Faltings height
2.4846
naive height
57.8272
primes of bad reduction
2, 3, 5, 7, 17
regulator
9.371923012302226390434740618139596382595
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)=(-12,5); 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=10710; local exponents {'2': 1, '3': 2, '5': 1, '7': 1, '17': 1}.

last edited by Natanael Wildner Fraga at · history

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