Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-225.2-a
Conductor 225.2
Rank \( 1 \)

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

Isogeny class 225.2-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
225.2-a1 \( \bigl[a\) , \( 0\) , \( a\) , \( 4 a - 15\) , \( -13 a + 28\bigr] \)
225.2-a2 \( \bigl[1\) , \( a - 1\) , \( 1\) , \( 6 a - 17\) , \( -18 a + 18\bigr] \)
225.2-a3 \( \bigl[1\) , \( a - 1\) , \( 1\) , \( a - 2\) , \( 0\bigr] \)
225.2-a4 \( \bigl[a\) , \( 0\) , \( a\) , \( -a\) , \( -a + 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph