Elliptic curve isogeny class 65.1-a over number field 3.3.169.1

• Base field: 3.3.169.1
• Label: 3.3.169.1-65.1-a
• Conductor: 65.1
• Rank: \( 1 \)

Base field 3.3.169.1

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

Elliptic curves in class 65.1-a over 3.3.169.1

Isogeny class 65.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
65.1-a1	\( \bigl[a + 1\) , \( 1\) , \( a^{2} - 3\) , \( -2 a^{2} - 2 a + 1\) , \( -4 a^{2} - 8 a - 4\bigr] \)
65.1-a2	\( \bigl[a + 1\) , \( 1\) , \( a^{2} - 3\) , \( -2 a^{2} + 3 a + 1\) , \( -8 a^{2} - 6 a - 3\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph