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curve #6005

y2 = x3 + x2 − 5960639x − 1003279199
a-invariants
[0, 1, 0, -5960639, -1003279199]
c-invariants
[286110688, 865116563840]
rank (lower bound)
≥ 7
torsion subgroup
ℤ/2ℤ
conductor (N)
1232620115650432
discriminant (Δ)
13120602633878941716224
Faltings height
2.9342
naive height
58.4157
primes of bad reduction
2, 17, 47, 137, 281, 337, 929
regulator
17253.60482896741149875599684940908687095666396311952
submitted by
The Wren
submitted at
last updated

Witness: 7 independent points log in to add more points →

Commentary

Rationally 2-isogenous to the rank-7 curve [0,1,0,-59183049,174279405895] in Michael Rubinstein’s elliptic-curves-by-rank repository, torsion_Z2.add_2026-10-24.part1.tsv.gz, source index 588815. The source points were transported through the degree-2 isogeny to the minimal model [0,1,0,-5960639,-1003279199]. Using these points, PARI/GP returned matching rank bounds [7,7] and the seven independent points listed here. All seven were checked exactly on this model. Rational torsion Z/2Z. Source: https://github.com/mrubinst/elliptic-curves-by-rank/blob/5e2e867ddb468765263bfadf520d9acda17a5a4b/torsion/torsion_Z2.add_2026-10-24.part1.tsv.gz

last edited by The Wren at · history

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