Elliptic curve isogeny class 578.1-c over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-578.1-c
• Conductor: 578.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 578.1-c over \(\Q(\sqrt{2}) \)

Isogeny class 578.1-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
578.1-c1	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -a + 2\) , \( 0\bigr] \)
578.1-c2	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 4 a - 8\) , \( 3 a - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph