Solutions of weierstrass equations

1979 ◽  
pp. 43-59
Author(s):  
David A. Cox
Keyword(s):  
Weierstrass Equations

ON j-INVARIANTS OF WEIERSTRASS EQUATIONS

2008 ◽  
Vol 45 (3) ◽  
pp. 695-698
Author(s):  
Ryutaro Horiuchi
Keyword(s):  
Weierstrass Equations

scholarly journals FORMAL GROUPS AND INVARIANT DIFFERENTIALS OF ELLIPTIC CURVES

2015 ◽  
Vol 92 (1) ◽  
pp. 44-51
Author(s):  
MOHAMMAD SADEK
Keyword(s):  
Power Series ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Series Expansion ◽  
Power Series Expansion ◽  
Formal Groups ◽  
Frobenius Endomorphism ◽  
Congruence Relations ◽  
Invariant Differential ◽  
Weierstrass Equations

In this paper, we find a power series expansion of the invariant differential ${\it\omega}_{E}$ of an elliptic curve $E$ defined over $\mathbb{Q}$, where $E$ is described by certain families of Weierstrass equations. In addition, we derive several congruence relations satisfied by the trace of the Frobenius endomorphism of $E$.

Weierstrass equations and the minimal discriminant of an elliptic curve

Mathematika ◽  
1984 ◽  
Vol 31 (2) ◽  
pp. 245-251 ◽  
Author(s):  
Joseph H. Silverman
Keyword(s):  
Elliptic Curve ◽  
Weierstrass Equations

scholarly journals Corrigendum to “A Schanuel Condition for Weierstrass Equations”

2005 ◽  
Vol 70 (3) ◽  
pp. 1023-1024
Author(s):  
Jonathan Kirby
Keyword(s):  
Weierstrass Equations

scholarly journals Isogenies on twisted Hessian curves

2021 ◽  
Vol 15 (1) ◽  
pp. 345-358
Author(s):  
Fouazou Lontouo Perez Broon ◽  
Thinh Dang ◽  
Emmanuel Fouotsa ◽  
Dustin Moody
Keyword(s):  
Elliptic Curves ◽  
Base Field ◽  
Explicit Formulas ◽  
Input Point ◽  
Weierstrass Equations

Abstract Elliptic curves are typically defined by Weierstrass equations. Given a kernel, the well-known Vélu's formula shows how to explicitly write down an isogeny between Weierstrass curves. However, it is not clear how to do the same on other forms of elliptic curves without isomorphisms mapping to and from the Weierstrass form. Previous papers have shown some isogeny formulas for (twisted) Edwards, Huff, and Montgomery forms of elliptic curves. Continuing this line of work, this paper derives explicit formulas for isogenies between elliptic curves in (twisted) Hessian form. In addition, we examine the numbers of operations in the base field to compute the formulas. In comparison with other isogeny formulas, we note that our formulas for twisted Hessian curves have the lowest costs for processing the kernel and our X-affine formula has the lowest cost for processing an input point in affine coordinates.

scholarly journals Weierstrass equations for Jacobian fibrations on a certain $K3$ surface

2012 ◽  
Vol 42 (3) ◽  
pp. 355-383 ◽  
Author(s):  
Kazuki Utsumi
Keyword(s):  
K3 Surface ◽  
Weierstrass Equations
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