Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-2178.1-b
Conductor 2178.1
Rank \( 1 \)

Related objects

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

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

Elliptic curves in class 2178.1-b over \(\Q(\sqrt{2}) \)

Isogeny class 2178.1-b contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
2178.1-b1 \( \bigl[1\) , \( 0\) , \( 0\) , \( -10055\) , \( -390309\bigr] \)
2178.1-b2 \( \bigl[1\) , \( 0\) , \( 0\) , \( 115\) , \( 561\bigr] \)
2178.1-b3 \( \bigl[1\) , \( 0\) , \( 0\) , \( -45\) , \( 81\bigr] \)
2178.1-b4 \( \bigl[1\) , \( 0\) , \( 0\) , \( -10065\) , \( -389499\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph