Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-180.3-a
Conductor 180.3
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 180.3-a over \(\Q(\sqrt{-11}) \)

Isogeny class 180.3-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
180.3-a1 \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -30 a - 246\) , \( 378 a + 1584\bigr] \)
180.3-a2 \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 30 a - 106\) , \( 174 a - 296\bigr] \)
180.3-a3 \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 4\) , \( 0\bigr] \)
180.3-a4 \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -16\) , \( 12 a + 28\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph