Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-6400.1-e
Conductor 6400.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{-3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 1 \); class number \(1\).

Elliptic curves in class 6400.1-e over \(\Q(\sqrt{-3}) \)

Isogeny class 6400.1-e contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
6400.1-e1 \( \bigl[0\) , \( 0\) , \( 0\) , \( -a\) , \( -4 a + 2\bigr] \)
6400.1-e2 \( \bigl[0\) , \( 0\) , \( 0\) , \( -41 a\) , \( -116 a + 58\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph