Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-12168.2-b
Conductor 12168.2
Rank \( 1 \)

Related objects

Learn more

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

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

Elliptic curves in class 12168.2-b over \(\Q(\sqrt{-2}) \)

Isogeny class 12168.2-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
12168.2-b1 \( \bigl[a\) , \( 1\) , \( a\) , \( 142\) , \( -3208\bigr] \)
12168.2-b2 \( \bigl[0\) , \( -1\) , \( 0\) , \( -651\) , \( 6228\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph