Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-9216.1-c
Conductor 9216.1
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 9216.1-c over \(\Q(\sqrt{-1}) \)

Isogeny class 9216.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
9216.1-c1 \( \bigl[0\) , \( i + 1\) , \( 0\) , \( 32 i\) , \( 360 i - 360\bigr] \)
9216.1-c2 \( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 2 i\) , \( 0\bigr] \)
9216.1-c3 \( \bigl[0\) , \( i + 1\) , \( 0\) , \( -8 i\) , \( -8 i + 8\bigr] \)
9216.1-c4 \( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -48 i\) , \( -72 i + 72\bigr] \)
9216.1-c5 \( \bigl[0\) , \( i + 1\) , \( 0\) , \( -128 i\) , \( -440 i + 440\bigr] \)
9216.1-c6 \( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -768 i\) , \( -5544 i + 5544\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph