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

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-870.4-a
• 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-a over \(\Q(\sqrt{6}) \)

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

Curve label	Weierstrass Coefficients
870.4-a1	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 4 a + 4\) , \( 4 a + 5\bigr] \)
870.4-a2	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 14 a - 76\) , \( 76 a - 223\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph