Elliptic curve isogeny class 729.4-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-729.4-a
• Conductor: 729.4
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-2}) \)

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

Elliptic curves in class 729.4-a over \(\Q(\sqrt{-2}) \)

Isogeny class 729.4-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
729.4-a1	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -2 a + 1\) , \( -a + 1\bigr] \)
729.4-a2	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -2 a - 5\) , \( -2 a - 3\bigr] \)
729.4-a3	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 13 a - 59\) , \( -68 a + 206\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)

Isogeny graph