Elliptic curve isogeny class 16.1-a over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-16.1-a
• Conductor: 16.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 16.1-a over \(\Q(\sqrt{6}) \)

Isogeny class 16.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
16.1-a1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4 a - 6\) , \( 6 a - 16\bigr] \)
16.1-a2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a - 6\) , \( -6 a - 16\bigr] \)
16.1-a3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 264 a - 646\) , \( 3782 a - 9264\bigr] \)
16.1-a4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -64 a - 166\) , \( 418 a + 1056\bigr] \)
16.1-a5	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 64 a - 166\) , \( -418 a + 1056\bigr] \)
16.1-a6	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -264 a - 646\) , \( -3782 a - 9264\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph