Elliptic curve isogeny class 726.1-d over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-726.1-d
• Conductor: 726.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 726.1-d over \(\Q(\sqrt{6}) \)

Isogeny class 726.1-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
726.1-d1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 811 a - 1984\) , \( -109228 a + 267554\bigr] \)
726.1-d2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 89 a + 221\) , \( -3920 a - 9601\bigr] \)
726.1-d3	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -111 a - 269\) , \( -952 a - 2331\bigr] \)
726.1-d4	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 1611 a - 3944\) , \( -54572 a + 133674\bigr] \)

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