Elliptic curve isogeny class 71.1-d over number field 6.6.485125.1

• Base field: 6.6.485125.1
• Label: 6.6.485125.1-71.1-d
• Conductor: 71.1
• 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 71.1-d over 6.6.485125.1

Isogeny class 71.1-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
71.1-d1	\( \bigl[a^{5} - 5 a^{3} + 5 a + 1\) , \( 3 a^{5} - 3 a^{4} - 14 a^{3} + 10 a^{2} + 11 a - 2\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 3 a + 1\) , \( 12 a^{5} - 14 a^{4} - 49 a^{3} + 42 a^{2} + 47 a - 13\) , \( 11 a^{5} - 6 a^{4} - 57 a^{3} + 38 a^{2} + 52 a - 24\bigr] \)
71.1-d2	\( \bigl[a^{5} - 5 a^{3} + 5 a + 1\) , \( 3 a^{5} - 3 a^{4} - 14 a^{3} + 10 a^{2} + 11 a - 2\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 3 a + 1\) , \( 12 a^{5} - 14 a^{4} - 54 a^{3} + 52 a^{2} + 52 a - 18\) , \( 15 a^{5} - 13 a^{4} - 64 a^{3} + 47 a^{2} + 54 a - 22\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph