Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-4356.5-a
Conductor 4356.5
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 4356.5-a over \(\Q(\sqrt{-7}) \)

Isogeny class 4356.5-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
4356.5-a1 \( \bigl[1\) , \( 0\) , \( 1\) , \( -41\) , \( -556\bigr] \)
4356.5-a2 \( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( 20\bigr] \)
4356.5-a3 \( \bigl[1\) , \( 0\) , \( 1\) , \( -6\) , \( 4\bigr] \)
4356.5-a4 \( \bigl[1\) , \( 0\) , \( 1\) , \( -81\) , \( -284\bigr] \)

Rank

Rank: \( 0 \)

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