Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-340.1-a
Conductor 340.1
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 340.1-a over \(\Q(\sqrt{-1}) \)

Isogeny class 340.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
340.1-a1 \( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( 7 i - 19\) , \( -17 i + 18\bigr] \)
340.1-a2 \( \bigl[0\) , \( i\) , \( 0\) , \( 2 i - 1\) , \( -i - 1\bigr] \)
340.1-a3 \( \bigl[0\) , \( i\) , \( 0\) , \( -18 i + 19\) , \( -13 i - 41\bigr] \)
340.1-a4 \( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( -3 i + 1\) , \( -i + 4\bigr] \)

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