Elliptic curve isogeny class 578.3-b over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-578.3-b
• Conductor: 578.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 578.3-b over \(\Q(\sqrt{2}) \)

Isogeny class 578.3-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
578.3-b1	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -843 a - 1849\) , \( 20550 a + 35806\bigr] \)
578.3-b2	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 67 a + 86\) , \( 139 a + 206\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph