Properties

Base field \(\Q(\sqrt{13}) \)
Label 2.2.13.1-1053.1-h
Conductor 1053.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{13}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 3 \); class number \(1\).

Elliptic curves in class 1053.1-h over \(\Q(\sqrt{13}) \)

Isogeny class 1053.1-h contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
1053.1-h1 \( \bigl[1\) , \( -1\) , \( 1\) , \( 2610 a - 6611\) , \( -105768 a + 250242\bigr] \)
1053.1-h2 \( \bigl[1\) , \( -1\) , \( 1\) , \( 4\) , \( 6\bigr] \)
1053.1-h3 \( \bigl[1\) , \( -1\) , \( 1\) , \( -41\) , \( 96\bigr] \)
1053.1-h4 \( \bigl[1\) , \( -1\) , \( 1\) , \( -176\) , \( -768\bigr] \)
1053.1-h5 \( \bigl[1\) , \( -1\) , \( 1\) , \( -626\) , \( 6180\bigr] \)
1053.1-h6 \( \bigl[1\) , \( -1\) , \( 1\) , \( -2610 a - 4001\) , \( 105768 a + 144474\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph