Tamagawa numbers of elliptic curves with prescribed torsion subgroup or isogeny
Antonela Trbovi\'c

TL;DR
This paper investigates Tamagawa numbers of elliptic curves with specific torsion subgroups over cubic fields and with certain isogenies over 9, revealing divisibility properties and exceptions related to their reduction types.
Contribution
It provides new divisibility results for Tamagawa numbers of elliptic curves with prescribed torsion or isogenies, extending understanding of their arithmetic properties.
Findings
Tamagawa numbers for curves with torsion Z/2ZZ/14Z over cubic fields are divisible by 14^2.
Elliptic curves with 18-isogeny have Tamagawa numbers divisible by 4.
Most other n-isogeny curves have Tamagawa numbers divisible by 2, with some exceptions.
Abstract
We study Tamagawa numbers of elliptic curves with torsion over cubic fields and of elliptic curves with an isogeny over , for . Bruin and Najman proved that every elliptic curve with torsion over a cubic field is a base change of an elliptic curve defined over . We find that Tamagawa numbers of elliptic curves defined over with torsion over a cubic field are always divisible by , with each factor coming from a rational prime with split multiplicative reduction of type one of which is always The only exception is the curve 1922.e2, with The same curves defined over cubic fields over which they…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
