Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-36864.2-b
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-b over \(\Q(\sqrt{-11}) \)

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

Curve label Weierstrass Coefficients
36864.2-b1 \( \bigl[0\) , \( -1\) , \( 0\) , \( 31\) , \( 33\bigr] \)
36864.2-b2 \( \bigl[0\) , \( -1\) , \( 0\) , \( -9\) , \( 9\bigr] \)
36864.2-b3 \( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( -2\bigr] \)
36864.2-b4 \( \bigl[0\) , \( -1\) , \( 0\) , \( -129\) , \( 609\bigr] \)

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