Computing All Elliptic Curves Over an Arbitrary Number Field with Prescribed Primes of Bad Reduction
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Publication:5743080
DOI10.1080/10586458.2017.1325791zbMath1443.11097arXiv1511.05108OpenAlexW2964131781MaRDI QIDQ5743080
Publication date: 8 May 2019
Published in: Experimental Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1511.05108
Related Items (8)
Black box Galois representations ⋮ Solving 𝑆-unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture ⋮ On the solutions of $x^p+y^p=2^rz^p$, $x^p+y^p=z^2$ over totally real fields ⋮ Quadratic fields admitting elliptic curves with rational \(j\)-invariant and good reduction everywhere ⋮ Computing elliptic curves over $\mathbb {Q}$ ⋮ On elliptic curves of prime power conductor over imaginary quadratic fields with class number 1 ⋮ Conductor and discriminant of Picard curves ⋮ On the solutions of the Diophantine equation \((x-d)^2 +x^2 +(x+d)^2 =y^n\) for \(d\) a prime power
Uses Software
Cites Work
- Solving exponential diophantine equations using lattice basis reduction algorithms
- On the practical solution of the Thue equation
- A modular construction of unramified p-extensions of \(\mathbb{Q}(\mu_p)\)
- On the solution of units and index form equations in algebraic number fields
- Improved Methods for Calculating Vectors of Short Length in a Lattice, Including a Complexity Analysis
- Solving a Specific Thue-Mahler Equation
- Determining the small solutions to 𝑆-unit equations
- The Solution of Triangularly Connected Decomposable Form Equations
- Finding All Elliptic Curves with Good Reduction Outside a Given Set of Primes
- Solving 𝑆-unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture
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