Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-4096.1-a
Conductor 4096.1
Rank \( 0 \)

Related objects

Learn more

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

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

Elliptic curves in class 4096.1-a over \(\Q(\sqrt{2}) \)

Isogeny class 4096.1-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
4096.1-a1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -1\) , \( -9 a - 13\bigr] \)
4096.1-a2 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -1\) , \( 9 a - 13\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph