Elliptic curve isogeny class 558.2-e over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-558.2-e
• Conductor: 558.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 558.2-e over \(\Q(\sqrt{2}) \)

Isogeny class 558.2-e contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
558.2-e1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 65 a - 178\) , \( -1424 a + 1450\bigr] \)
558.2-e2	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 109 a + 145\) , \( 431 a + 619\bigr] \)