Elliptic curve isogeny class 441.2-c over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-441.2-c
• Conductor: 441.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 441.2-c over \(\Q(\sqrt{2}) \)

Isogeny class 441.2-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
441.2-c1	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 2\) , \( 0\bigr] \)
441.2-c2	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -6 a - 17\) , \( 14 a + 28\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph