Elliptic curve isogeny class 432.4-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-432.4-a
• Conductor: 432.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 432.4-a over \(\Q(\sqrt{-2}) \)

Isogeny class 432.4-a contains 4 curves linked by isogenies of degrees dividing 27.

Curve label	Weierstrass Coefficients
432.4-a1	\( \bigl[a\) , \( -a\) , \( a\) , \( a - 3\) , \( 2 a - 1\bigr] \)
432.4-a2	\( \bigl[a\) , \( -a\) , \( 0\) , \( 2 a - 2\) , \( 2\bigr] \)
432.4-a3	\( \bigl[a\) , \( -a\) , \( a\) , \( 201 a + 277\) , \( -974 a + 2839\bigr] \)
432.4-a4	\( \bigl[a\) , \( -a\) , \( a\) , \( 41 a + 17\) , \( -58 a - 141\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 9 & 3 \\ 3 & 1 & 27 & 9 \\ 9 & 27 & 1 & 3 \\ 3 & 9 & 3 & 1 \end{array}\right)\)

Isogeny graph