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curve #1374

y2 + xy + y = x3 + x2 − 1702849424631976406x + 815433058060520543741414099
a-invariants
[1, 1, 1, -1702849424631976406, 815433058060520543741414099]
rank (lower bound)
≥ 10
torsion subgroup
ℤ/2ℤ
conductor (N)
274041685980626458099814310
discriminant (Δ)
28765516653337068029166786181779192222185057587943178240
Faltings height
9.3986
naive height
137.5501
primes of bad reduction
2, 3, 5, 13, 41, 83, 101, 157, 163, 313, 389, 409, 613, 2617
regulator
14476581915.47603780881857213181004219961152466385778786441
submitted by
jesper-petersen
submitted at
last updated

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Commentary

Obtained by taking a rational 2-isogenous quotient of curve #1203, submitted by Noam Elkies, which has rank at least 10 and torsion \(\mathbf Z/2\mathbf Z\times\mathbf Z/2\mathbf Z\). Quotienting by one of its rational 2-torsion points gives \(y^2=x^3+10590663569x^2+10141794149802983424x\). Its global minimal model has ainvs \([1,1,1,-1702849424631976406,815433058060520543741414099]\), torsion \(\mathbf Z/2\mathbf Z\), and the same conductor \(274041685980626458099814310\). The ten independent points on #1203 were mapped through the 2-isogeny, giving ten independent points on the quotient; the construction and invariants were verified in Magma.

last edited by jesper-petersen at · history

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