Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-17424.5-d
Conductor 17424.5
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 17424.5-d over \(\Q(\sqrt{-2}) \)

Isogeny class 17424.5-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
17424.5-d1 \( \bigl[a\) , \( 1\) , \( 0\) , \( -1994\) , \( -35226\bigr] \)
17424.5-d2 \( \bigl[a\) , \( 1\) , \( 0\) , \( 1550 a - 1914\) , \( -55576 a - 46786\bigr] \)
17424.5-d3 \( \bigl[a\) , \( 1\) , \( 0\) , \( -1550 a - 1914\) , \( 55576 a - 46786\bigr] \)
17424.5-d4 \( \bigl[a\) , \( 1\) , \( 0\) , \( -2004\) , \( -34866\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph