Elliptic curve isogeny class 96.1-d over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-96.1-d
• Conductor: 96.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 96.1-d over \(\Q(\sqrt{6}) \)

Isogeny class 96.1-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
96.1-d1	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -135 a - 335\) , \( 2080 a + 5094\bigr] \)
96.1-d2	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -40 a + 98\) , \( -198 a + 485\bigr] \)
96.1-d3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -2\) , \( 0\bigr] \)
96.1-d4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -86 a - 210\) , \( -774 a - 1896\bigr] \)
96.1-d5	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -160 a - 395\) , \( 1485 a + 3636\bigr] \)
96.1-d6	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 135 a - 335\) , \( -2080 a + 5094\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph