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Equivalent of integralQuarticPoints from Magma in Sage?

asked 2023-09-16 15:37:23 +0200

Bike gravatar image

In Magma there is a function integralQuarticPoints that can be used to get all the integer solutions to $$ y^2 = ax^4+bx^3+cx^2+dx+e $$ when $e$ is a square. There is a function .integral_points() for ElipticCurves, but this is a quartic not an eliptic curve.

Is there a way to do this in Sage?

PS: Would have added link to the docs of the Magma function, but not allowed to due insufficient karma.

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answered 2023-09-17 17:20:20 +0200

Max Alekseyev gravatar image

To best of my knowledge, there is no such equivalent. You can find details about IntegralQuarticPoints implementation in the comments to this MO answer. So, until someone implements the same in Sage, the only option is to use Sage's interface to Magma.

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Asked: 2023-09-16 15:37:23 +0200

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Last updated: Sep 17