Elliptic curve isogeny class 162.1-f over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-162.1-f
• Conductor: 162.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{6}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 6 \); class number \(1\).

Elliptic curves in class 162.1-f over \(\Q(\sqrt{6}) \)

Isogeny class 162.1-f contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
162.1-f1	\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 64 a - 152\) , \( 378 a - 923\bigr] \)
162.1-f2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -14\) , \( 29\bigr] \)
162.1-f3	\( \bigl[1\) , \( -1\) , \( 1\) , \( 1\) , \( -1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph