Elliptic curve isogeny class 256.1-f over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-256.1-f
• Conductor: 256.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 256.1-f over \(\Q(\sqrt{6}) \)

Isogeny class 256.1-f contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
256.1-f1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( a - 3\bigr] \)
256.1-f2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( a + 3\bigr] \)
256.1-f3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -10 a - 23\) , \( 35 a + 86\bigr] \)
256.1-f4	\( \bigl[0\) , \( -a\) , \( 0\) , \( 10 a - 23\) , \( 35 a - 86\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph