Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-784.1-b
Conductor 784.1
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 784.1-b over \(\Q(\sqrt{-2}) \)

Isogeny class 784.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
784.1-b1 \( \bigl[a\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
784.1-b2 \( \bigl[a\) , \( -1\) , \( 0\) , \( -14\) , \( -10\bigr] \)
784.1-b3 \( \bigl[a\) , \( -1\) , \( 0\) , \( -4\) , \( 6\bigr] \)
784.1-b4 \( \bigl[a\) , \( -1\) , \( 0\) , \( -74\) , \( 286\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph