Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-16900.2-e
Conductor 16900.2
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 16900.2-e over \(\Q(\sqrt{-7}) \)

Isogeny class 16900.2-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
16900.2-e1 \( \bigl[1\) , \( -1\) , \( 1\) , \( -67\) , \( -441\bigr] \)
16900.2-e2 \( \bigl[1\) , \( -1\) , \( 1\) , \( -7\) , \( -1\bigr] \)
16900.2-e3 \( \bigl[1\) , \( -1\) , \( 1\) , \( -87\) , \( -289\bigr] \)
16900.2-e4 \( \bigl[1\) , \( -1\) , \( 1\) , \( -1387\) , \( -19529\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph