Elliptic curve isogeny class 900.1-c over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-900.1-c
• Conductor: 900.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 900.1-c over \(\Q(\sqrt{2}) \)

Isogeny class 900.1-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
900.1-c1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a - 3\) , \( -5 a + 8\bigr] \)
900.1-c2	\( \bigl[a\) , \( a\) , \( a\) , \( -10 a - 16\) , \( -20 a - 28\bigr] \)