Quadratic fields admitting elliptic curves with rational \(j\)-invariant and good reduction everywhere

DOI10.1016/j.jnt.2022.11.003OpenAlexW3136594886MaRDI QIDQ2689523

Benjamin Matschke, Abhijit S. Mudigonda

Publication date: 10 March 2023

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.09814

zbMATH Keywords

quadratic fieldsTauberian theoremszeta functionselliptic curves over global fieldsmultiplicative number theorygood reduction of elliptic curves

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05)

Uses Software

• Magma
• PARI/GP
• SageMath

Cites Work

• When the sieve works
• Explicit bounds for primes in arithmetic progressions
• Elliptic curves over real quadratic fields with everywhere good reduction and a non-trivial 3-division point
• Elliptic curves with trivial conductor over quadratic fields
• Modular invariant and good reduction of elliptic curves
• Elliptic curves with everywhere good reduction
• Grandes valeurs de la fonction somme des diviseurs et hypothèse de Riemann
• Elliptic curves with good reduction everywhere over quadratic fields and having rational \(j\)-invariant
• Reduction of elliptic curves over imaginary quadratic number fields
• Divisibilite de certaines fonctions arithmétiques
• Elliptic curves over complex quadratic fields
• The non-existence of elliptic curves with everywhere good reduction over certain imaginary quadratic fields
• The Magma algebra system. I: The user language
• Nonexistence of elliptic curves with good reduction everywhere over real quadratic fields
• Family of elliptic curves with good reduction everywhere over number fields of given degree
• Good reduction of elliptic curves over imaginary quadratic fields
• Potential good reduction of elliptic curves.
• When the sieve works. II
• A refinement of theabcconjecture
• The Arithmetic of Elliptic Curves
• Corrigendum to the paper "Elementary methods in the theory of L-functions, VII. Upper bound for L(1,χ)"
• Reduction of elliptic curves over certain real quadratic number fields
• Baker's explicit abc-conjecture and applications
• Upper Bounds for  L(1,  )
• Elliptic curves with good reduction everywhere over cubic fields
• Rational and Integral Points on Quadratic Twists of a Given Hyperelliptic Curve
• Finding All Elliptic Curves with Good Reduction Outside a Given Set of Primes
• Computing All Elliptic Curves Over an Arbitrary Number Field with Prescribed Primes of Bad Reduction
• Nonexistence of elliptic curves having everywhere good reduction and cubic discriminant
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