Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-16200.2-d
Conductor 16200.2
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 16200.2-d over \(\Q(\sqrt{-1}) \)

Isogeny class 16200.2-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
16200.2-d1 \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i - 9\) , \( -9 i\bigr] \)
16200.2-d2 \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 36\) , \( -18 i\bigr] \)
16200.2-d3 \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 306\) , \( 2196 i\bigr] \)
16200.2-d4 \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 486\) , \( -3888 i\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph