Elliptic curve isogeny class 5.1-a over number field 4.4.8069.1

• Base field: 4.4.8069.1
• Label: 4.4.8069.1-5.1-a
• Conductor: 5.1
• Rank: \( 0 \)

Base field 4.4.8069.1

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

Elliptic curves in class 5.1-a over 4.4.8069.1

Isogeny class 5.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
5.1-a1	\( \bigl[a^{2} + a - 2\) , \( 0\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 5 a^{3} - 5 a^{2} - 9 a - 6\) , \( a^{3} - 21 a^{2} + 40 a + 3\bigr] \)
5.1-a2	\( \bigl[a^{2} + a - 2\) , \( 0\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a - 1\) , \( a^{3} - 3 a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph