Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-100.1-a
Conductor 100.1
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 100.1-a over \(\Q(\sqrt{-2}) \)

Isogeny class 100.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
100.1-a1 \( \bigl[a\) , \( 0\) , \( a\) , \( -8\) , \( 18\bigr] \)
100.1-a2 \( \bigl[a\) , \( 0\) , \( a\) , \( 2\) , \( 0\bigr] \)
100.1-a3 \( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \)
100.1-a4 \( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph