Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-40000.3-e
Conductor 40000.3
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 40000.3-e over \(\Q(\sqrt{-1}) \)

Isogeny class 40000.3-e contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
40000.3-e1 \( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( 16 i + 19\) , \( 16 i - 47\bigr] \)
40000.3-e2 \( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( -18 i + 19\) , \( -17 i - 47\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph