Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-19602.1-e
Conductor 19602.1
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 19602.1-e over \(\Q(\sqrt{-1}) \)

Isogeny class 19602.1-e contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
19602.1-e1 \( \bigl[i\) , \( 1\) , \( i\) , \( -1324\) , \( -4969\bigr] \)
19602.1-e2 \( \bigl[i\) , \( 1\) , \( i\) , \( -64\) , \( -209\bigr] \)
19602.1-e3 \( \bigl[i\) , \( 1\) , \( i\) , \( -784\) , \( 8207\bigr] \)
19602.1-e4 \( \bigl[i\) , \( 1\) , \( i\) , \( -1024\) , \( -12881\bigr] \)

Rank

Rank: \( 1 \)

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