Elliptic curve isogeny class 41.1-a over number field 6.6.485125.1

• Base field: 6.6.485125.1
• Label: 6.6.485125.1-41.1-a
• Conductor: 41.1
• 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 41.1-a over 6.6.485125.1

Isogeny class 41.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
41.1-a1	\( \bigl[-a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 4 a\) , \( -3 a^{5} + 4 a^{4} + 13 a^{3} - 14 a^{2} - 9 a + 6\) , \( a^{2} + a - 2\) , \( -a^{4} + 3 a^{3} - 4 a^{2} - 3 a + 3\) , \( -4 a^{5} + 6 a^{4} + 11 a^{3} - 12 a^{2} - 10 a + 3\bigr] \)
41.1-a2	\( \bigl[a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 7 a^{2} + a + 5\) , \( 1\) , \( -a^{5} + 4 a^{4} + 2 a^{3} - 14 a^{2} - a + 10\) , \( -2 a^{5} + 4 a^{4} + 7 a^{3} - 13 a^{2} - 5 a + 8\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph