Properties

Base field \(\Q(\sqrt{53}) \)
Label 2.2.53.1-196.1-f
Conductor 196.1
Rank not recorded

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 196.1-f over \(\Q(\sqrt{53}) \)

Isogeny class 196.1-f contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
196.1-f1 \( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \)
196.1-f2 \( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \)
196.1-f3 \( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \)
196.1-f4 \( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \)
196.1-f5 \( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \)
196.1-f6 \( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph