Elliptic curve isogeny class 64.1-a over number field 6.6.485125.1

• Base field: 6.6.485125.1
• Label: 6.6.485125.1-64.1-a
• Conductor: 64.1
• Rank: \( 1 \)

Base field 6.6.485125.1

Generator \(a\), with minimal polynomial \( x^{6} - 2 x^{5} - 4 x^{4} + 8 x^{3} + 2 x^{2} - 5 x + 1 \); class number \(1\).

Elliptic curves in class 64.1-a over 6.6.485125.1

Isogeny class 64.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
64.1-a1	\( \bigl[a^{4} - 3 a^{2} + 1\) , \( -a^{5} + 5 a^{3} - 5 a\) , \( a^{2} - 1\) , \( a^{5} - 3 a^{3} - a^{2} + 2 a + 1\) , \( 2 a^{5} - 7 a^{3} + 4 a - 1\bigr] \)
64.1-a2	\( \bigl[a^{4} - 3 a^{2} - a + 1\) , \( a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + a + 1\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 8 a - 2\) , \( -4 a^{4} + 16 a^{2} + a - 5\) , \( 4 a^{5} - 5 a^{4} - 17 a^{3} + 18 a^{2} + 9 a - 12\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph