Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-257.1-a
Conductor 257.1
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 257.1-a over \(\Q(\sqrt{-1}) \)

Isogeny class 257.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
257.1-a1 \( \bigl[i\) , \( -i\) , \( 1\) , \( 5\) , \( 3 i - 1\bigr] \)
257.1-a2 \( \bigl[i\) , \( -i\) , \( 1\) , \( -5 i + 5\) , \( 4 i - 12\bigr] \)
257.1-a3 \( \bigl[1\) , \( i\) , \( i\) , \( 0\) , \( 0\bigr] \)
257.1-a4 \( \bigl[i\) , \( -i\) , \( 1\) , \( 5 i + 85\) , \( 274 i - 34\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph