Properties

Base field \(\Q(\sqrt{53}) \)
Label 2.2.53.1-17.1-a
Conductor 17.1
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 17.1-a over \(\Q(\sqrt{53}) \)

Isogeny class 17.1-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
17.1-a1 \( \bigl[1\) , \( -1\) , \( 0\) , \( 4 a + 12\) , \( -3 a - 9\bigr] \)
17.1-a2 \( \bigl[1\) , \( -1\) , \( 0\) , \( -a - 3\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph