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curve #3369

y2 + xy = x3 − 2919020660x + 60845521107600
a-invariants
[1, 0, 0, -2919020660, 60845521107600]
rank (lower bound)
≥ 2
torsion subgroup
ℤ/7ℤ
conductor (N)
13422930
discriminant (Δ)
-7542518754050368634880000000
Faltings height
4.2226
naive height
77.0019
primes of bad reduction
2, 3, 5, 19, 23549
regulator
10.2195833769297217083158645549767764869076
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/7ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with b=t^3-t^2, c=t^2-t, at t = 24/19; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 13422930, torsion ℤ/7ℤ.

last edited by David Renshaw at · history

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