Elliptic curves with nonsplit mod 11 representations
نویسندگان
چکیده
We calculate explicitly the j-invariants of the elliptic curves corresponding to rational points on the modular curve X+ ns(11) by giving an expression defined over Q of the j-function in terms of the function field generators X and Y of the elliptic curve X+ ns(11). As a result we exhibit infinitely many elliptic curves over Q with nonsplit mod 11 representations.
منابع مشابه
Mod 2 Representations of Elliptic Curves
Explicit equations are given for the elliptic curves (in characteristic 6= 2, 3) with mod 2 representation isomorphic to that of a given one.
متن کاملMod 2 Representations of Elliptic Curves
Explicit equations are given for the elliptic curves (in characteristic = 2, 3) with mod 2 representation isomorphic to that of a given one.
متن کاملMod 4 Galois Representations and Elliptic Curves
Galois representations ρ : GQ → GL2(Z/n) with cyclotomic determinant all arise from the n-torsion of elliptic curves for n = 2, 3, 5. For n = 4, we show the existence of more than a million such representations which are surjective and do not arise from any elliptic curve.
متن کاملMOD p REPRESENTATIONS ON ELLIPTIC CURVES
Modular Galois representations ρ : Gal(Q/Q) → GL2(Fp) with cyclotomic determinant arise from elliptic curves for small p. We show that ρ does not necessarily arise from an elliptic curve whose conductor is as small as possible outside p. For p = 3 this disproves a conjecture of J. Lario and A. Rio [8].
متن کاملDrinfeld Modules with No Supersingular Primes
We give examples of Drinfeld modules φ of rank 2 and higher over Fq(T ) that have no primes of supersingular reduction. The idea is to construct φ so that the associated mod ` representations are incompatible with the existence of supersingular primes. We also answer a question of Elkies by proving that such obstructions cannot exist for elliptic curves over number fields. Elkies [El1] proved t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Math. Comput.
دوره 73 شماره
صفحات -
تاریخ انتشار 2004