Elliptic curve isogeny class 144.1-b over number field \(\Q(\sqrt{69}) \)

• Base field: \(\Q(\sqrt{69}) \)
• Label: 2.2.69.1-144.1-b
• Conductor: 144.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 144.1-b over \(\Q(\sqrt{69}) \)

Isogeny class 144.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
144.1-b1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 1872 a - 8711\bigr] \)
144.1-b2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 1\bigr] \)
144.1-b3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -1125 a - 4110\) , \( -41184 a - 150458\bigr] \)
144.1-b4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -15\) , \( 22\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph