scholarly journals Bounds for Serre’s open image theorem for elliptic curves over number fields

2015 ◽  
Vol 9 (10) ◽  
pp. 2347-2395 ◽  
Author(s):  
Davide Lombardo
Keyword(s):  
Elliptic Curves ◽  
Number Fields ◽  
Image Theorem

scholarly journals Darmon points on elliptic curves over number fields of arbitrary signature

2015 ◽  
Vol 111 (2) ◽  
pp. 484-518 ◽  
Author(s):  
Xavier Guitart ◽  
Marc Masdeu ◽  
Mehmet Haluk Şengün
Keyword(s):  
Elliptic Curves ◽  
Number Fields ◽  
Arbitrary Signature

scholarly journals Bounds on $2$-torsion in class groups of number fields and integral points on elliptic curves

2020 ◽  
Vol 33 (4) ◽  
pp. 1087-1099 ◽  
Author(s):  
M. Bhargava ◽  
A. Shankar ◽  
T. Taniguchi ◽  
F. Thorne ◽  
J. Tsimerman ◽  
...  
Keyword(s):  
Elliptic Curves ◽  
Number Fields ◽  
Class Groups ◽  
Integral Points

scholarly journals LOCAL HEIGHTS ON ELLIPTIC CURVES AND INTERSECTION MULTIPLICITIES

2012 ◽  
Vol 08 (06) ◽  
pp. 1477-1484
Author(s):  
VINCENZ BUSCH ◽  
JAN STEFFEN MÜLLER
Keyword(s):  
Elliptic Curves ◽  
Short Note ◽  
Number Fields ◽  
Intersection Theory ◽  
Ring Of Integers ◽  
Regular Model ◽  
Intersection Multiplicities

In this short note we prove a formula for local heights on elliptic curves over number fields in terms of intersection theory on a regular model over the ring of integers.

scholarly journals ON THE NUMBER OF ELLIPTIC CURVES WITH PRESCRIBED ISOGENY OR TORSION GROUP OVER NUMBER FIELDS OF PRIME DEGREE

2014 ◽  
Vol 57 (2) ◽  
pp. 465-473 ◽  
Author(s):  
FILIP NAJMAN
Keyword(s):  
Elliptic Curves ◽  
Number Field ◽  
Torsion Group ◽  
Number Fields ◽  
Prime Degree

AbstractLet p be a prime and K a number field of degree p. We determine the finiteness of the number of elliptic curves, up to K-isomorphism, having a prescribed property, where this property is either that the curve contains a fixed torsion group as a subgroup or that it has a cyclic isogeny of prescribed degree.

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