Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-57600.1-g
Conductor 57600.1
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 57600.1-g over \(\Q(\sqrt{-3}) \)

Isogeny class 57600.1-g contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
57600.1-g1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 109\) , \( -731 a + 420\bigr] \)
57600.1-g2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 11\) , \( 13 a - 12\bigr] \)
57600.1-g3 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 4\) , \( 4 a\bigr] \)
57600.1-g4 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 124\) , \( -572 a + 348\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph