Elliptic curve isogeny class 882.1-b over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-882.1-b
• Conductor: 882.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 882.1-b over \(\Q(\sqrt{2}) \)

Isogeny class 882.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
882.1-b1	\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( a - 1\) , \( a - 1\bigr] \)
882.1-b2	\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 16 a - 31\) , \( 49 a - 67\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph