Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-4032.4-a
Conductor 4032.4
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 4032.4-a over \(\Q(\sqrt{-7}) \)

Isogeny class 4032.4-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
4032.4-a1 \( \bigl[0\) , \( 1\) , \( 0\) , \( 48\) , \( 48\bigr] \)
4032.4-a2 \( \bigl[0\) , \( 1\) , \( 0\) , \( -12\) , \( 0\bigr] \)
4032.4-a3 \( \bigl[0\) , \( 1\) , \( 0\) , \( -7\) , \( -10\bigr] \)
4032.4-a4 \( \bigl[0\) , \( 1\) , \( 0\) , \( -152\) , \( 672\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph