Elliptic curve isogeny class 43.1-a over number field 4.4.1957.1

• Base field: 4.4.1957.1
• Label: 4.4.1957.1-43.1-a
• Conductor: 43.1
• Rank: \( 1 \)

Base field 4.4.1957.1

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

Elliptic curves in class 43.1-a over 4.4.1957.1

Isogeny class 43.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
43.1-a1	\( \bigl[a^{2} - 1\) , \( 2 a^{3} - a^{2} - 8 a\) , \( 0\) , \( -3 a^{3} + 3 a^{2} + 10 a - 7\) , \( -a^{3} - 2 a^{2} + 4 a + 9\bigr] \)
43.1-a2	\( \bigl[1\) , \( -a - 1\) , \( a^{2} - a - 1\) , \( a\) , \( -a^{2} + a + 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph