Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-578.2-a
Conductor 578.2
Rank \( 0 \)

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 578.2-a over \(\Q(\sqrt{-1}) \)

Isogeny class 578.2-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
578.2-a1 \( \bigl[i\) , \( 0\) , \( 0\) , \( -3\) , \( -1\bigr] \)
578.2-a2 \( \bigl[i\) , \( 0\) , \( 0\) , \( -113\) , \( 329\bigr] \)
578.2-a3 \( \bigl[i\) , \( 0\) , \( 0\) , \( -43\) , \( -105\bigr] \)
578.2-a4 \( \bigl[i\) , \( 0\) , \( 0\) , \( -103\) , \( 411\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph