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curve #1376

y2 + xy = x3 − 305209366509156400979315990x + 2052318850802631274310734280222290328100
a-invariants
[1, 0, 0, -305209366509156400979315990, 2052318850802631274310734280222290328100]
rank (lower bound)
≥ 5
torsion subgroup
ℤ/2ℤ × ℤ/4ℤ
conductor (N)
3985472961137327010
discriminant (Δ)
549437270678590464225302075768679959302976257913234650728960000000000000000
Faltings height
13.7386
naive height
194.5627
primes of bad reduction
2, 3, 5, 13, 17, 29, 31, 43, 173, 257, 367, 953
regulator
2448563.93456964265401889943293416031346244785215
submitted by
jesper-petersen
submitted at
last updated

Witness: 5 independent points log in to add more points →

Commentary

Obtained from curve #1093, due to Dujella–Lecacheux, which has rank at least 5 and torsion \(\mathbf Z/8\mathbf Z\). Quotienting by its rational point of order 2 gives a 2-isogenous curve whose global minimal model has ainvs \([1,0,0,-305209366509156400979315990,2052318850802631274310734280222290328100]\), torsion \(\mathbf Z/2\mathbf Z\times\mathbf Z/4\mathbf Z\), and conductor \(3985472961137327010\). The five independent source points were mapped through the isogeny, yielding five independent points on the quotient. The isogeny, minimal model, conductor, torsion and image points were verified in Magma.

last edited by jesper-petersen at · history

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