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

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-162.1-a
• Conductor: 162.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
162.1-a1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \)
162.1-a2	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -273 a - 666\) , \( -5520 a - 13522\bigr] \)
162.1-a3	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -26 a + 66\) , \( -54 a + 134\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph