Elliptic curve isogeny class 289.1-d over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-289.1-d
• Conductor: 289.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 289.1-d over \(\Q(\sqrt{6}) \)

Isogeny class 289.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
289.1-d1	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 14 a - 32\) , \( -2766 a + 6777\bigr] \)
289.1-d2	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -13 a - 29\) , \( -38 a - 94\bigr] \)
289.1-d3	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 114 a - 277\) , \( -1131 a + 2772\bigr] \)
289.1-d4	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -1813 a - 4439\) , \( 63142 a + 154666\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph