"isogeny" meaning in All languages combined

{
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      "_dis1": "0 0",
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      "_dis1": "0 0",
      "word": "isogenic"
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          "ref": "2000, Marc Hindry, Joseph H. Silverman, Diophantine Geometry: An Introduction, Springer, page 95:",
          "text": "It is clear that if G#x5F;2 is connected, then two of the defining properties of an isogeny imply the third.",
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          "text": "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,\nLemma 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."
        },
        {
          "text": "2005, Fred Diamond, Jerry Shurman, A First Course in Modular Forms, Springer, page 29,\nThe 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\nφ∘̂φ=[ operatorname deg(φ)]=[ operatorname deg(̂φ)],\nso 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."
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        {
          "_dis1": "6 94",
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          "word": "isogenia"
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    "isogeny"
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