Elliptic curve isogeny class 67.2-a over number field 6.6.592661.1

• Base field: 6.6.592661.1
• Label: 6.6.592661.1-67.2-a
• Conductor: 67.2
• Rank: \( 1 \)

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 67.2-a over 6.6.592661.1

Isogeny class 67.2-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
67.2-a1	\( \bigl[a^{5} - a^{4} - 4 a^{3} + 5 a^{2} + 2 a - 4\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 8 a^{2} + 5 a - 3\) , \( 2 a^{5} - a^{4} - 9 a^{3} + 4 a^{2} + 6 a - 3\) , \( 4 a^{5} - 3 a^{4} - 19 a^{3} + 11 a^{2} + 14 a - 6\) , \( a^{5} - a^{4} - 6 a^{3} + 3 a^{2} + 6 a - 3\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph