Elliptic curve isogeny class 7.1-a over number field 6.6.592661.1

• Base field: 6.6.592661.1
• Label: 6.6.592661.1-7.1-a
• Conductor: 7.1
• Rank: \( 0 \)

Base field 6.6.592661.1

Generator \(a\), with minimal polynomial \( x^{6} - x^{5} - 5 x^{4} + 4 x^{3} + 5 x^{2} - 2 x - 1 \); class number \(1\).

Elliptic curves in class 7.1-a over 6.6.592661.1

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

Curve label	Weierstrass Coefficients
7.1-a1	\( \bigl[a^{4} - 3 a^{2} + a - 1\) , \( -a^{5} + a^{4} + 4 a^{3} - 5 a^{2} - a + 5\) , \( a\) , \( -8 a^{5} + 11 a^{4} + 31 a^{3} - 43 a^{2} - 9 a + 9\) , \( -21 a^{5} + 25 a^{4} + 63 a^{3} - 113 a^{2} + 14 a + 21\bigr] \)
7.1-a2	\( \bigl[a^{2} + a - 2\) , \( a^{2} - a - 2\) , \( a^{4} - 4 a^{2} + a + 1\) , \( 2 a^{4} - 2 a^{3} - 7 a^{2} + 4 a + 2\) , \( a^{4} - 5 a^{2} + a + 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph