Elliptic curve isogeny class 13.1-a over number field 4.4.4205.1

• Base field: 4.4.4205.1
• Label: 4.4.4205.1-13.1-a
• Conductor: 13.1
• Rank: \( 1 \)

Base field 4.4.4205.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 5 x^{2} - x + 1 \); class number \(1\).

Elliptic curves in class 13.1-a over 4.4.4205.1

Isogeny class 13.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
13.1-a1	\( \bigl[a^{2} - 2 a - 1\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( a^{2} - a - 2\) , \( a^{3} - a^{2} - 3 a\) , \( -a^{2} - 2 a - 1\bigr] \)
13.1-a2	\( \bigl[a^{2} - a - 1\) , \( -a - 1\) , \( a^{2} - 2 a - 1\) , \( 2 a^{3} - 4 a^{2} - 7 a + 2\) , \( -2 a^{3} + 3 a^{2} + 9 a - 4\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph