Elliptic curve isogeny class 873.1-c over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-873.1-c
• Conductor: 873.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 873.1-c over \(\Q(\sqrt{2}) \)

Isogeny class 873.1-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
873.1-c1	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 5 a - 9\) , \( 12 a - 13\bigr] \)
873.1-c2	\( \bigl[a\) , \( a\) , \( 1\) , \( 18 a - 38\) , \( 67 a - 85\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph