Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-86.4-a
Conductor 86.4
Rank \( 0 \)

Related objects

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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 86.4-a over \(\Q(\sqrt{-7}) \)

Isogeny class 86.4-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
86.4-a1 \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 4 a + 9\) , \( 17 a - 13\bigr] \)
86.4-a2 \( \bigl[a\) , \( a + 1\) , \( 1\) , \( -a - 111\) , \( -110 a - 352\bigr] \)
86.4-a3 \( \bigl[a\) , \( a + 1\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph