Elliptic curve isogeny class 784.1-f over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-784.1-f
• Conductor: 784.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 784.1-f over \(\Q(\sqrt{6}) \)

Isogeny class 784.1-f contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
784.1-f1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -682\) , \( -6990\bigr] \)
784.1-f2	\( \bigl[a\) , \( -1\) , \( 0\) , \( -2\) , \( 2\bigr] \)
784.1-f3	\( \bigl[a\) , \( -1\) , \( 0\) , \( 18\) , \( -46\bigr] \)
784.1-f4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -142\) , \( -558\bigr] \)
784.1-f5	\( \bigl[a\) , \( -1\) , \( 0\) , \( -42\) , \( 98\bigr] \)
784.1-f6	\( \bigl[a\) , \( -1\) , \( 0\) , \( -10922\) , \( -441166\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph