Properties

Base field \(\Q(\sqrt{53}) \)
Label 2.2.53.1-289.1-f
Conductor 289.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{53}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 13 \); class number \(1\).

Elliptic curves in class 289.1-f over \(\Q(\sqrt{53}) \)

Isogeny class 289.1-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
289.1-f1 \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \)
289.1-f2 \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \)
289.1-f3 \( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \)
289.1-f4 \( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \)

Rank

Rank: \( 0 \)

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