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

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-578.1-g
• Conductor: 578.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
578.1-g1	\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( -16\) , \( 11 a - 29\bigr] \)
578.1-g2	\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( -5 a - 6\) , \( -7 a - 11\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph