Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-57600.1-r
Conductor 57600.1
Rank \( 0 \)

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 57600.1-r over \(\Q(\sqrt{-3}) \)

Isogeny class 57600.1-r contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
57600.1-r1 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -10 a + 11\) , \( 11 a - 11\bigr] \)
57600.1-r2 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 50 a - 49\) , \( 47 a + 1\bigr] \)
57600.1-r3 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 410 a - 409\) , \( -3769 a + 2089\bigr] \)
57600.1-r4 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 650 a - 649\) , \( 7127 a - 3239\bigr] \)

Rank

Rank: \( 0 \)

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