Elliptic curve isogeny class 288.1-d over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-288.1-d
• Conductor: 288.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 288.1-d over \(\Q(\sqrt{2}) \)

Isogeny class 288.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
288.1-d1	\( \bigl[0\) , \( a\) , \( 0\) , \( -1\) , \( -3 a\bigr] \)
288.1-d2	\( \bigl[a\) , \( -1\) , \( a\) , \( -50 a - 73\) , \( 4 a + 6\bigr] \)
288.1-d3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -11\) , \( -7 a\bigr] \)
288.1-d4	\( \bigl[a\) , \( 0\) , \( a\) , \( 50 a - 73\) , \( 4 a - 7\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph