Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-289.2-a
Conductor 289.2
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 289.2-a over \(\Q(\sqrt{-1}) \)

Isogeny class 289.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
289.2-a1 \( \bigl[i\) , \( 1\) , \( i\) , \( 0\) , \( 14\bigr] \)
289.2-a2 \( \bigl[i\) , \( 1\) , \( i\) , \( 0\) , \( 0\bigr] \)
289.2-a3 \( \bigl[i\) , \( 1\) , \( i\) , \( -75 i + 40\) , \( -38 i + 304\bigr] \)
289.2-a4 \( \bigl[i\) , \( 1\) , \( i\) , \( 75 i + 40\) , \( 38 i + 304\bigr] \)
289.2-a5 \( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \)
289.2-a6 \( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 4 & 2 & 2 & 2 & 4 \\ 4 & 1 & 8 & 8 & 2 & 4 \\ 2 & 8 & 1 & 4 & 4 & 8 \\ 2 & 8 & 4 & 1 & 4 & 8 \\ 2 & 2 & 4 & 4 & 1 & 2 \\ 4 & 4 & 8 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph