Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-1458.1-t
Conductor 1458.1
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 1458.1-t over \(\Q(\sqrt{2}) \)

Isogeny class 1458.1-t contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
1458.1-t1 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -31 a - 54\) , \( -44 a - 44\bigr] \)
1458.1-t2 \( \bigl[1\) , \( -1\) , \( a\) , \( 67 a - 258\) , \( -1296 a + 1074\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph