Properties

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

Isogeny class 57600.1-i contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
57600.1-i1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -240 a\) , \( -14400 a + 7200\bigr] \)
57600.1-i2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 240 a\) , \( 480 a - 240\bigr] \)
57600.1-i3 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -60 a\) , \( 0\bigr] \)
57600.1-i4 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -600 a\) , \( -6912 a + 3456\bigr] \)
57600.1-i5 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -45 a\) , \( 108 a - 54\bigr] \)
57600.1-i6 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -9600 a\) , \( -424512 a + 212256\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph