Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-15876.3-e
Conductor 15876.3
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 15876.3-e over \(\Q(\sqrt{-11}) \)

Isogeny class 15876.3-e contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
15876.3-e1 \( \bigl[1\) , \( -1\) , \( 1\) , \( -1535\) , \( 23591\bigr] \)
15876.3-e2 \( \bigl[1\) , \( -1\) , \( 1\) , \( -5\) , \( -7\bigr] \)
15876.3-e3 \( \bigl[1\) , \( -1\) , \( 1\) , \( 40\) , \( 155\bigr] \)
15876.3-e4 \( \bigl[1\) , \( -1\) , \( 1\) , \( -320\) , \( 1883\bigr] \)
15876.3-e5 \( \bigl[1\) , \( -1\) , \( 1\) , \( -95\) , \( -331\bigr] \)
15876.3-e6 \( \bigl[1\) , \( -1\) , \( 1\) , \( -24575\) , \( 1488935\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph