Properties

Base field \(\Q(\sqrt{53}) \)
Label 2.2.53.1-1764.1-a
Conductor 1764.1
Rank \( 1 \)

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 1764.1-a over \(\Q(\sqrt{53}) \)

Isogeny class 1764.1-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
1764.1-a1 \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 3 a + 10\) , \( 51 a + 160\bigr] \)
1764.1-a2 \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -87 a - 280\) , \( 679 a + 2140\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph