Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-4096.1-a
Conductor 4096.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{-1}) \)

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

Elliptic curves in class 4096.1-a over \(\Q(\sqrt{-1}) \)

Isogeny class 4096.1-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
4096.1-a1 \( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( 1\bigr] \)
4096.1-a2 \( \bigl[0\) , \( i\) , \( 0\) , \( 3\) , \( -i\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph