Elliptic curve isogeny class 71.1-b over number field 6.6.485125.1

• Base field: 6.6.485125.1
• Label: 6.6.485125.1-71.1-b
• 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-b over 6.6.485125.1

Isogeny class 71.1-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
71.1-b1	\( \bigl[-a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 3 a + 2\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 4 a + 1\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 8 a - 3\) , \( a^{5} + a^{4} - 10 a^{3} + 4 a^{2} + 10 a - 2\) , \( -2 a^{5} + 5 a^{4} + 4 a^{3} - 10 a^{2} - 4 a + 3\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph