Elliptic curve isogeny class 121.1-a over number field \(\Q(\sqrt{69}) \)

• Base field: \(\Q(\sqrt{69}) \)
• Label: 2.2.69.1-121.1-a
• Conductor: 121.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{69}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 17 \); class number \(1\).

Elliptic curves in class 121.1-a over \(\Q(\sqrt{69}) \)

Isogeny class 121.1-a contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
121.1-a1	\( \bigl[0\) , \( -1\) , \( 1\) , \( -586525 a - 2142771\) , \( 498496619 a + 1821163667\bigr] \)
121.1-a2	\( \bigl[0\) , \( -1\) , \( 1\) , \( 775 a - 3606\) , \( -43609 a + 202926\bigr] \)
121.1-a3	\( \bigl[0\) , \( -1\) , \( 1\) , \( 25 a - 116\) , \( 321 a - 1494\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph