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

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-600.1-d
• 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-d over \(\Q(\sqrt{6}) \)

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

Curve label	Weierstrass Coefficients
600.1-d1	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 77 a + 185\) , \( -127866 a - 313208\bigr] \)
600.1-d2	\( \bigl[a\) , \( -1\) , \( a\) , \( 210 a - 517\) , \( -2546 a + 6235\bigr] \)
600.1-d3	\( \bigl[a\) , \( -1\) , \( a\) , \( 20 a - 52\) , \( 10 a - 26\bigr] \)
600.1-d4	\( \bigl[a\) , \( -1\) , \( a\) , \( 230 a - 567\) , \( 3006 a - 7365\bigr] \)
600.1-d5	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6 a - 13\) , \( 21 a + 52\bigr] \)
600.1-d6	\( \bigl[a\) , \( -1\) , \( a\) , \( 140 a - 357\) , \( 5280 a - 12951\bigr] \)

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