Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-2450.1-g
Conductor 2450.1
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 2450.1-g over \(\Q(\sqrt{2}) \)

Isogeny class 2450.1-g contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
2450.1-g1 \( \bigl[1\) , \( a\) , \( 1\) , \( -a\) , \( -2\bigr] \)
2450.1-g2 \( \bigl[1\) , \( a\) , \( 1\) , \( -6 a - 20\) , \( -24 a - 42\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph