Elliptic curve isogeny class 870.4-y over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-870.4-y
• Conductor: 870.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 870.4-y over \(\Q(\sqrt{6}) \)

Isogeny class 870.4-y contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
870.4-y1	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 70 a - 259\) , \( -1286 a + 4867\bigr] \)
870.4-y2	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 5 a - 9\) , \( 17 a - 45\bigr] \)
870.4-y3	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 5 a - 29\) , \( 5 a - 9\bigr] \)
870.4-y4	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 85 a - 379\) , \( -797 a + 2869\bigr] \)
870.4-y5	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -75 a + 1\) , \( -281 a - 183\bigr] \)
870.4-y6	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 1380 a - 6099\) , \( -58836 a + 199743\bigr] \)

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