Elliptic curves of conductor $11$
نویسندگان
چکیده
منابع مشابه
On elliptic curves of conductor 11 2 and an open question of Ihara
In previous work, joint with Tamagawa, the author investigated a certain class of elliptic curves with constrained prime power torsion. If an open question of Ihara has an affirmative answer, then the prime power torsion of such curves must be rational over the fixed field Ωl of the canonical outer pro-l Galois representation attached to P01∞. This is indeed the case for most examples. In the c...
متن کاملElliptic Curves of Large Rank and Small Conductor
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 over 100 (for r = 10 and r = 11). We describe our search methods, and tabulate, for each r = 5, 6, . . . , 11, the five curves of lowest conductor, and (except for r = 11) also the five of lowest absolute disc...
متن کاملElliptic curves with nonsplit mod 11 representations
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.
متن کاملMazur ’ s question on mod 11 representations of elliptic curves ∗
The main idea of the proof of this Theorem is to study the geometry (and arithmetic) of the modular diagonal quotient surfaces ZN,1 (as introduced in [9]) in the special case N = 11. Now the algebraic surface Z = ZN,1 has a natural model as a variety over Q (cf. §3), and an open subvariety of this turns out to be the coarse moduli space of the moduli functor ZN,1 which classifies isomorphism cl...
متن کاملOn Silverman's conjecture for a family of elliptic curves
Let $E$ be an elliptic curve over $Bbb{Q}$ with the given Weierstrass equation $ y^2=x^3+ax+b$. If $D$ is a squarefree integer, then let $E^{(D)}$ denote the $D$-quadratic twist of $E$ that is given by $E^{(D)}: y^2=x^3+aD^2x+bD^3$. Let $E^{(D)}(Bbb{Q})$ be the group of $Bbb{Q}$-rational points of $E^{(D)}$. It is conjectured by J. Silverman that there are infinitely many primes $p$ for which $...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1980
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1980-0572871-5