Properties

Base field \(\Q(\sqrt{53}) \)
Label 2.2.53.1-900.1-f
Conductor 900.1
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 900.1-f over \(\Q(\sqrt{53}) \)

Isogeny class 900.1-f contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
900.1-f1 \( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -64\bigr] \)
900.1-f2 \( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \)
900.1-f3 \( \bigl[1\) , \( 0\) , \( 1\) , \( -454\) , \( -544\bigr] \)
900.1-f4 \( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \)
900.1-f5 \( \bigl[1\) , \( 0\) , \( 1\) , \( -19\) , \( 26\bigr] \)
900.1-f6 \( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \)
900.1-f7 \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \)
900.1-f8 \( \bigl[1\) , \( 0\) , \( 1\) , \( -5334\) , \( -150368\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph