Elliptic curve isogeny class 256.1-d over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-256.1-d
• Conductor: 256.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 256.1-d over \(\Q(\sqrt{2}) \)

Isogeny class 256.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
256.1-d1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 1\bigr] \)
256.1-d2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 10 a - 22\) , \( -36 a + 46\bigr] \)
256.1-d3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 2\bigr] \)
256.1-d4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -10 a - 22\) , \( 36 a + 46\bigr] \)

Rank

Rank: \( 1 \)

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