Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-16731.2-b
Conductor 16731.2
Rank \( 2 \)

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 16731.2-b over \(\Q(\sqrt{-11}) \)

Isogeny class 16731.2-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
16731.2-b1 \( \bigl[1\) , \( 0\) , \( 0\) , \( -24\) , \( 63\bigr] \)
16731.2-b2 \( \bigl[1\) , \( 0\) , \( 0\) , \( 1341\) , \( 18228\bigr] \)
16731.2-b3 \( \bigl[1\) , \( 0\) , \( 0\) , \( -474\) , \( 2619\bigr] \)
16731.2-b4 \( \bigl[1\) , \( 0\) , \( 0\) , \( -3009\) , \( -61770\bigr] \)
16731.2-b5 \( \bigl[1\) , \( 0\) , \( 0\) , \( -429\) , \( 3384\bigr] \)
16731.2-b6 \( \bigl[1\) , \( 0\) , \( 0\) , \( -6864\) , \( 218313\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph