Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-218.2-a
Conductor 218.2
Rank \( 0 \)

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Base field \(\Q(\sqrt{-7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 2 \); class number \(1\).

Elliptic curves in class 218.2-a over \(\Q(\sqrt{-7}) \)

Isogeny class 218.2-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
218.2-a1 \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 179 a - 350\) , \( 1720 a - 1930\bigr] \)
218.2-a2 \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -a\) , \( 0\bigr] \)
218.2-a3 \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 4 a - 5\) , \( -a - 4\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph