Elliptic curve isogeny class 400.1-d over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-400.1-d
• Conductor: 400.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 400.1-d over \(\Q(\sqrt{6}) \)

Isogeny class 400.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
400.1-d1	\( \bigl[a\) , \( 0\) , \( 0\) , \( 65 a + 160\) , \( 874 a + 2141\bigr] \)
400.1-d2	\( \bigl[a\) , \( 0\) , \( 0\) , \( -35 a - 85\) , \( 131 a + 321\bigr] \)
400.1-d3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( -1\bigr] \)
400.1-d4	\( \bigl[a\) , \( 0\) , \( 0\) , \( 535 a - 1310\) , \( -10276 a + 25171\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph