Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-36864.2-x
Conductor 36864.2
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{-11}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 3 \); class number \(1\).

Elliptic curves in class 36864.2-x over \(\Q(\sqrt{-11}) \)

Isogeny class 36864.2-x contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
36864.2-x1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 321 a - 850\) , \( -5032 a + 7403\bigr] \)
36864.2-x2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -319 a - 530\) , \( -5352 a - 2901\bigr] \)
36864.2-x3 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 50\) , \( -200 a + 75\bigr] \)
36864.2-x4 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 30\) , \( -24 a + 27\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph