Elliptic curve isogeny class 67.2-b over number field 6.6.592661.1

• Base field: 6.6.592661.1
• Label: 6.6.592661.1-67.2-b
• 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-b over 6.6.592661.1

Isogeny class 67.2-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
67.2-b1	\( \bigl[2 a^{5} - a^{4} - 9 a^{3} + 5 a^{2} + 5 a - 5\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 6 a - 2\) , \( a^{2} - 1\) , \( -4 a^{5} + 17 a^{3} - a^{2} - 6 a + 6\) , \( 11 a^{5} - 4 a^{4} - 60 a^{3} + 5 a^{2} + 70 a + 26\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph