isogeny
Word Rarity
Very rare
Frequency: Zipf frequency 0.00 in modern English
11
Scrabble Score
7
Letters
2
Syllables
7
Unique Chars
Meaning
noun
An epimorphism of group schemes that is surjective and has a finite kernel.
Countable; Uncountable
Example Sentences
- "It is clear that if G#95;2 is connected, then two of the defining properties of an isogeny imply the third."
- "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."
Etymology
From iso- + -geny.
Word Breakdown
Usage
Inflected Forms
Derived Forms
Phrases
dual isogeny
isogeny cycle
isogeny graph
isogeny volcano