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curve #3357

y2 + xy = x3 − 100491064135x + 11888352025002761
a-invariants
[1, 0, 0, -100491064135, 11888352025002761]
rank (lower bound)
≥ 2
torsion subgroup
ℤ/10ℤ
conductor (N)
34172754
discriminant (Δ)
3891575873940612631257756769846272
Faltings height
5.2168
naive height
87.6136
primes of bad reduction
2, 3, 7, 11, 17, 19, 229
regulator
7.13243867876757806571475553326540344733731
submitted by
David Renshaw
submitted at
last updated

Witness: 2 independent points log in to add more points →

Commentary

Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/10ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with d=t^2/(t-(t-1)^2), c=td-t, b=cd, at t = 14/17; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 34172754, torsion ℤ/10ℤ.

last edited by David Renshaw at · history

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