Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-36864.1-c
Conductor 36864.1
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 36864.1-c over \(\Q(\sqrt{-3}) \)

Isogeny class 36864.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
36864.1-c1 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -115 a + 128\) , \( -58 a - 563\bigr] \)
36864.1-c2 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 5 a + 8\) , \( 14 a - 35\bigr] \)
36864.1-c3 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 5 a - 7\) , \( 5 a - 2\bigr] \)
36864.1-c4 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 125 a + 128\) , \( 902 a - 1379\bigr] \)

Rank

Rank: \( 1 \)

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