Elliptic curve isogeny class 2592.1-e over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-2592.1-e
• Conductor: 2592.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 2592.1-e over \(\Q(\sqrt{2}) \)

Isogeny class 2592.1-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
2592.1-e1	\( \bigl[a\) , \( 1\) , \( 0\) , \( 18\) , \( 27\bigr] \)
2592.1-e2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -21\) , \( 20\bigr] \)
2592.1-e3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -92\bigr] \)
2592.1-e4	\( \bigl[a\) , \( 1\) , \( a\) , \( -73\) , \( 202\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph