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

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-600.1-a
• Conductor: 600.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
600.1-a1	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -90 a - 226\) , \( 39852 a + 97622\bigr] \)
600.1-a2	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -20 a + 49\) , \( 0\bigr] \)
600.1-a3	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 80 a - 196\) , \( 396 a - 970\bigr] \)
600.1-a4	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 680 a - 1666\) , \( -13860 a + 33950\bigr] \)
600.1-a5	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -1080 a - 2646\) , \( -32076 a - 78570\bigr] \)
600.1-a6	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 90 a - 226\) , \( -39852 a + 97622\bigr] \)

Rank

Rank: \( 1 \)

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