Elliptic curve isogeny class 7.1-a over number field 4.4.4205.1

• Base field: 4.4.4205.1
• Label: 4.4.4205.1-7.1-a
• Conductor: 7.1
• Rank: \( 0 \)

Base field 4.4.4205.1

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

Elliptic curves in class 7.1-a over 4.4.4205.1

Isogeny class 7.1-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
7.1-a1	\( \bigl[a^{2} - a - 1\) , \( a^{2} - 3 a - 3\) , \( 0\) , \( 8 a^{3} - 16 a^{2} - 20 a - 4\) , \( 24 a^{3} - 80 a^{2} + 14 a + 49\bigr] \)
7.1-a2	\( \bigl[a^{2} - a - 1\) , \( a^{2} - 3 a - 3\) , \( 0\) , \( -2 a^{3} + 4 a^{2} + 5 a + 1\) , \( 0\bigr] \)
7.1-a3	\( \bigl[a + 1\) , \( -2 a^{3} + 3 a^{2} + 8 a\) , \( a\) , \( 10 a^{3} - 21 a^{2} - 23 a - 1\) , \( -7 a^{3} + 31 a^{2} - 28 a - 32\bigr] \)
7.1-a4	\( \bigl[a + 1\) , \( -2 a^{3} + 3 a^{2} + 8 a\) , \( a\) , \( -a^{2} + 2 a + 4\) , \( 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph