Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-99.2-a
Conductor 99.2
Rank \( 0 \)

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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 99.2-a over \(\Q(\sqrt{-11}) \)

Isogeny class 99.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
99.2-a1 \( \bigl[1\) , \( 1\) , \( 0\) , \( 44\) , \( 55\bigr] \)
99.2-a2 \( \bigl[1\) , \( 1\) , \( 0\) , \( -11\) , \( 0\bigr] \)
99.2-a3 \( \bigl[1\) , \( 1\) , \( 0\) , \( -6\) , \( -9\bigr] \)
99.2-a4 \( \bigl[1\) , \( 1\) , \( 0\) , \( -50 a + 509\) , \( 2414 a + 58\bigr] \)
99.2-a5 \( \bigl[1\) , \( 1\) , \( 0\) , \( 50 a + 459\) , \( -2414 a + 2472\bigr] \)
99.2-a6 \( \bigl[1\) , \( 1\) , \( 0\) , \( -146\) , \( 621\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph