Elliptic curve isogeny class 600.1-h over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-600.1-h
• Conductor: 600.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 600.1-h over \(\Q(\sqrt{6}) \)

Isogeny class 600.1-h contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
600.1-h1	\( \bigl[a\) , \( 1\) , \( a\) , \( 110 a - 275\) , \( 1046 a - 2769\bigr] \)
600.1-h2	\( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \)
600.1-h3	\( \bigl[a\) , \( 1\) , \( a\) , \( -5\) , \( -3\bigr] \)
600.1-h4	\( \bigl[a\) , \( 1\) , \( a\) , \( -35\) , \( -105\bigr] \)
600.1-h5	\( \bigl[a\) , \( 1\) , \( a\) , \( -55\) , \( 107\bigr] \)
600.1-h6	\( \bigl[a\) , \( 1\) , \( a\) , \( -110 a - 275\) , \( -1046 a - 2769\bigr] \)

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