Elliptic curve isogeny class 288.2-d over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-288.2-d
• Conductor: 288.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 288.2-d over \(\Q(\sqrt{-2}) \)

Isogeny class 288.2-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
288.2-d1	\( \bigl[a\) , \( 0\) , \( 0\) , \( -5 a + 22\) , \( -26 a - 23\bigr] \)
288.2-d2	\( \bigl[a\) , \( 0\) , \( 0\) , \( 5 a + 22\) , \( 26 a - 23\bigr] \)
288.2-d3	\( \bigl[a\) , \( 0\) , \( 0\) , \( 2\) , \( -1\bigr] \)
288.2-d4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -2\) , \( 0\bigr] \)
288.2-d5	\( \bigl[0\) , \( 1\) , \( 0\) , \( -4\) , \( 2\bigr] \)
288.2-d6	\( \bigl[a\) , \( 0\) , \( a\) , \( -7\) , \( -7\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 4 & 2 & 4 & 8 & 8 \\ 4 & 1 & 2 & 4 & 8 & 8 \\ 2 & 2 & 1 & 2 & 4 & 4 \\ 4 & 4 & 2 & 1 & 2 & 2 \\ 8 & 8 & 4 & 2 & 1 & 4 \\ 8 & 8 & 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph