Elliptic curve isogeny class 7.1-a over number field 4.4.8789.1

• Base field: 4.4.8789.1
• Label: 4.4.8789.1-7.1-a
• Conductor: 7.1
• Rank: \( 1 \)

Base field 4.4.8789.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 6 x^{2} - 2 x + 1 \); class number \(1\).

Elliptic curves in class 7.1-a over 4.4.8789.1

Isogeny class 7.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
7.1-a1	\( \bigl[a\) , \( -a^{3} + 2 a^{2} + 3 a\) , \( 0\) , \( -72 a^{3} + 192 a^{2} + 112 a - 44\) , \( -422 a^{3} + 1125 a^{2} + 658 a - 254\bigr] \)
7.1-a2	\( \bigl[a^{3} - 2 a^{2} - 3 a + 2\) , \( -a^{3} + 2 a^{2} + 5 a - 1\) , \( a + 1\) , \( -11 a^{3} + 20 a^{2} + 52 a - 17\) , \( 32 a^{3} - 54 a^{2} - 153 a + 44\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph