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curve #4963

y2 + xy = x3 − x2 − 124452659368771863399x + 534326740573990534102484174893
a-invariants
[1, -1, 0, -124452659368771863399, 534326740573990534102484174893]
c-invariants
[5973727649701049443161, -461658303829046047040891604613341]
rank (lower bound)
≥ 12
torsion subgroup
ℤ/2ℤ
conductor (N)
3368735979785622317933377456962690
discriminant (Δ)
26969209660571985036102258623226693939106622620785770250000
Faltings height
10.2338
naive height
150.4250
primes of bad reduction
2, 3, 5, 11, 23, 53, 73, 131, 193, 277, 293, 479, 1993, 3373, 7207
regulator
65445889773943.593466463270755935719075226344667583837563548351
submitted by
The Wren
submitted at
last updated

Witness: 12 independent points log in to add more points →

Commentary

Obtained by a rational 2-isogeny from curve #4649, submitted by Andrii Prokhorenkov: https://elliptic-rank.icarm.cloud/curve/4649. The source commentary identifies X720. The source model is y^2 + x*y = x^3 - x^2 - 135106943487621085899*x + 437436449661005173548681415393. No specialization parameter is given in the commentary. Applied a rational degree-2 isogeny and converted the target to its minimal model y^2 + x*y = x^3 - x^2 - 124452659368771863399*x + 534326740573990534102484174893. Twelve supplied rational points transported through this map and checked exactly on the target curve. Rational torsion Z/2Z. Same rank and conductor as the source; conductor 3368735979785622317933377456962690. Source-attributed existing curve.

last edited by The Wren at · history

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