Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-19208.1-d
Conductor 19208.1
Rank \( 2 \)

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 19208.1-d over \(\Q(\sqrt{-2}) \)

Isogeny class 19208.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
19208.1-d1 \( \bigl[a\) , \( -1\) , \( a\) , \( 14\) , \( 80\bigr] \)
19208.1-d2 \( \bigl[a\) , \( -1\) , \( a\) , \( -721\) , \( -5555\bigr] \)
19208.1-d3 \( \bigl[a\) , \( -1\) , \( a\) , \( -231\) , \( 1403\bigr] \)
19208.1-d4 \( \bigl[a\) , \( -1\) , \( a\) , \( -3661\) , \( 87153\bigr] \)

Rank

Rank: \( 2 \)

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