Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-784.3-a
Conductor 784.3
Rank \( 1 \)

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

Isogeny class 784.3-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
784.3-a1 \( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 1\bigr] \)
784.3-a2 \( \bigl[0\) , \( -1\) , \( 0\) , \( -142\) , \( 701\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph