Elliptic Curve Isogeny Class 16.1-a over Number Field 4.4.725.1

• Base field: 4.4.725.1
• Label: 4.4.725.1-16.1-a
• Conductor: 16.1
• Rank: not recorded

Base field 4.4.725.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 3 x^{2} + x + 1 \); class number \(1\).

Elliptic curves in class 16.1-a over 4.4.725.1

Isogeny class 16.1-a contains 2 curves linked by isogenies of degree 17.

Curve label	Weierstrass Coefficients
16.1-a1	\( \bigl[a^{3} - 2 a\) , \( a^{2} - 2 a - 1\) , \( a^{2}\) , \( -a^{3} + a^{2} + a\) , \( 0\bigr] \)
16.1-a2	\( \bigl[a^{3} - 2 a\) , \( a^{2} - 2 a - 1\) , \( a^{2}\) , \( -651 a^{3} - 699 a^{2} + 651 a\) , \( -22754 a^{3} - 25330 a^{2} + 18130 a + 8832\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 17 \\ 17 & 1 \end{array}\right)\)

Isogeny graph