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

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-870.4-f
• Conductor: 870.4
• Rank: \( 1 \)

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

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

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

Isogeny class 870.4-f contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
870.4-f1	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 809910 a - 1991312\) , \( -622507027 a + 1525064612\bigr] \)
870.4-f2	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 290 a - 692\) , \( -6927 a + 16892\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph