Elliptic curve isogeny class 24.1-a over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-24.1-a
• Conductor: 24.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 24.1-a over \(\Q(\sqrt{6}) \)

Isogeny class 24.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
24.1-a1	\( \bigl[a\) , \( -1\) , \( a\) , \( 1\) , \( 21\bigr] \)
24.1-a2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -14 a + 35\) , \( 67 a - 164\bigr] \)
24.1-a3	\( \bigl[a\) , \( -1\) , \( a\) , \( -4\) , \( -2\bigr] \)
24.1-a4	\( \bigl[a\) , \( -1\) , \( a\) , \( -9\) , \( 3\bigr] \)
24.1-a5	\( \bigl[a\) , \( -1\) , \( a\) , \( -19\) , \( -29\bigr] \)
24.1-a6	\( \bigl[a\) , \( -1\) , \( a\) , \( -99\) , \( 345\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph