478 citations
- Harvard UniversityUS5 papers
- University of California, BerkeleyUS3 papers
- Bar-Ilan UniversityIL2 papers
- Brookhaven National LaboratoryUS2 papers
- CEA Paris-SaclayFR2 papers
- Center for Astrophysics Harvard & SmithsonianUS2 papers
- Commissariat à l'Énergie Atomique et aux Énergies AlternativesFR2 papers
- Universidad de JaénES2 papers
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- Astrophysique, Instrumentation et ModélisationFR1 paper
- Australian National UniversityAU1 paper
- Berkeley CollegeUS1 paper
4 papers · 1 filter
Elliptic Curves x^3 + y^3 = k of High Rank
Noam D. Elkies, Nicholas F. Rogers
We use rational parametrizations of certain cubic surfaces and an explicit formula for descent via 3-isogeny to construct the first examples of elliptic curves E_k: x^3 + y^3 = k o…
Elliptic curves of large rank and small conductor
Noam D. Elkies, Mark Watkins
For r=6,7,...,11 we find an elliptic curve E/Q of rank at least r and the smallest conductor known, improving on the previous records by factors ranging from 1.0136 (for r=6) to ov…
On the Ramification of Hecke Algebras at Eisenstein Primes
Frank Calegari, Matthew Emerton
Using the modularity technique of Wiles, we study the Hecke algebra of weight 2 and prime level N localized at the Eisenstein primes. On the way, we recover some results of Mazur (…
Slopes of overconvergent 2-adic modular forms
Kevin Buzzard, Frank Calegari
The slope of a p-adic overconvergent eigenform of weight k is the p-adic valuation of its U_p eigenvalue. We find the slope of all 2-adic finite slope overconvergent eigenforms of…