Elliptic curve isogeny class 8.1-a over number field 3.3.169.1

• Base field: 3.3.169.1
• Label: 3.3.169.1-8.1-a
• Conductor: 8.1
• Rank: \( 0 \)

Base field 3.3.169.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 4 x - 1 \); class number \(1\).

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 8.1-a over 3.3.169.1

Isogeny class 8.1-a contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
8.1-a1	\( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{2} - a - 2\) , \( 149 a^{2} - 150 a - 657\) , \( 1719 a^{2} - 1999 a - 6787\bigr] \)
8.1-a2	\( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{2} - a - 2\) , \( -a^{2} + 3\) , \( -a^{2} + a + 3\bigr] \)