Elliptic curve isogeny class 83.1-b over number field 6.6.592661.1

• Base field: 6.6.592661.1
• Label: 6.6.592661.1-83.1-b
• Conductor: 83.1
• 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 83.1-b over 6.6.592661.1

Isogeny class 83.1-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
83.1-b1	\( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 4 a - 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 4\) , \( 2 a^{5} - a^{4} - 9 a^{3} + 4 a^{2} + 5 a - 2\) , \( 3 a^{5} - 14 a^{3} - a^{2} + 10 a + 1\) , \( -3 a^{5} - a^{4} + 13 a^{3} + 6 a^{2} - 5 a - 4\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph