Meaning

The condition of being isogenous..

Definitions by Sense

1. The condition of being isogenous.
2. (algebraic geometry, category theory) An epimorphism of group schemes that is surjective and has a finite kernel.

Example Sentences

2002, Mireille Fouquet, François Morain, Isogeny Volcanoes and the SEA Algorithm, Claus Fieker, David R. Kohel (editors), Algorithmic Number Theory: 5th International Symposium, Proceedings, Springer, LNCS 2369, page 279, Lemma 2.2 Let E be an elliptic curve such that Z [π] is maximal at 𝓁. If there exists an 𝓁-isogeny of E, then this 𝓁-isogeny is an horizontal 𝓁-isogeny.

2005, Fred Diamond, Jerry Shurman, A First Course in Modular Forms, Springer, page 29, The dual isogeny of an isomorphism is its inverse. The dual of a composition of isogenies is the composition of the duals in the reverse order. If φ is an isogeny and ̂φ is its dual then the formulas φ(z+Λ)=mz+Λ', φ(z'+Λ')=( operatorname φ/m)z'+Λ show that also φ∘̂φ=[ operatorname deg(φ)]=[ operatorname deg(̂φ)], so that φ is in turn the dual isogeny of its dual ̂φ. Isogeny of complex tori, rather than isomorphism, will turn out to be the appropriate equivalence relation in the context of modular forms.

It is clear that if G#95;2 is connected, then two of the defining properties of an isogeny imply the third.

Word Forms

• isogenies

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When Should You Use Isogeny?

Use isogeny when its meaning, tone and grammar fit the full sentence. A synonym is not always a direct replacement.

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