Elliptic curve isogeny class 4418.1-d over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-4418.1-d
• Conductor: 4418.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 4418.1-d over \(\Q(\sqrt{2}) \)

Isogeny class 4418.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
4418.1-d1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 0\) , \( -1\bigr] \)
4418.1-d2	\( \bigl[1\) , \( -1\) , \( 1\) , \( 45 a - 90\) , \( 260 a - 325\bigr] \)
4418.1-d3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -10\) , \( -9\bigr] \)
4418.1-d4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -45 a - 90\) , \( -260 a - 325\bigr] \)

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