Elliptic curve isogeny class 267.3-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-267.3-a
• Conductor: 267.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 267.3-a over \(\Q(\sqrt{-2}) \)

Isogeny class 267.3-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
267.3-a1	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 156 a - 170\) , \( 1221 a - 332\bigr] \)
267.3-a2	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 3 a + 8\) , \( -5 a + 7\bigr] \)
267.3-a3	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 38 a - 42\) , \( -166 a + 48\bigr] \)
267.3-a4	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( a\) , \( 2 a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph