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

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

Isogeny class 870.4-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
870.4-d1	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -869 a - 2121\) , \( 20258 a + 49618\bigr] \)
870.4-d2	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -9 a - 21\) , \( 14 a + 34\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph