Elliptic curve isogeny class 71.1-a over number field 4.4.2624.1

• Base field: 4.4.2624.1
• Label: 4.4.2624.1-71.1-a
• Conductor: 71.1
• Rank: \( 1 \)

Base field 4.4.2624.1

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

Elliptic curves in class 71.1-a over 4.4.2624.1

Isogeny class 71.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
71.1-a1	\( \bigl[a^{3} - a^{2} - 3 a\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - a + 1\) , \( 2 a^{3} - 6 a - 1\) , \( 2 a^{3} - 3 a - 1\bigr] \)
71.1-a2	\( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( -a^{3} + 2 a^{2} + 3 a - 2\) , \( a + 1\) , \( -a^{2} + a + 2\) , \( -a - 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph