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

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-578.1-e
• 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-e over \(\Q(\sqrt{2}) \)

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

Curve label	Weierstrass Coefficients
578.1-e1	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 4 a - 6\) , \( 7 a - 11\bigr] \)
578.1-e2	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -a - 16\) , \( -11 a - 29\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph