Elliptic curve isogeny class 7.1-a over number field 4.4.16317.1

• Base field: 4.4.16317.1
• Label: 4.4.16317.1-7.1-a
• Conductor: 7.1
• Rank: \( 1 \)

Base field 4.4.16317.1

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

Elliptic curves in class 7.1-a over 4.4.16317.1

Isogeny class 7.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
7.1-a1	\( \bigl[a^{3} - 5 a - 2\) , \( a^{2} - a - 4\) , \( a + 1\) , \( 110 a^{3} - 56 a^{2} - 577 a - 264\) , \( -1122 a^{3} + 699 a^{2} + 5798 a + 2036\bigr] \)
7.1-a2	\( \bigl[a^{3} - 5 a - 2\) , \( a^{2} - a - 4\) , \( a + 1\) , \( -a^{2} + 3 a + 6\) , \( a^{3} - a^{2} - 2 a + 1\bigr] \)
7.1-a3	\( \bigl[a^{3} - 5 a - 2\) , \( a^{2} - a - 4\) , \( a + 1\) , \( 10 a^{3} - 46 a^{2} + 48 a + 6\) , \( 67 a^{3} - 296 a^{2} + 314 a - 39\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph