Properties

Base field \(\Q(\sqrt{57}) \)
Label 2.2.57.1-16.3-a
Conductor 16.3
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{57}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 14 \); class number \(1\).

Elliptic curves in class 16.3-a over \(\Q(\sqrt{57}) \)

Isogeny class 16.3-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
16.3-a1 \( \bigl[a\) , \( a - 1\) , \( a\) , \( -882 a - 2893\) , \( 27153 a + 88921\bigr] \)
16.3-a2 \( \bigl[a\) , \( -a\) , \( 0\) , \( -320 a + 1368\) , \( -469916 a + 2008852\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph