Properties

Base field \(\Q(\sqrt{13}) \)
Label 2.2.13.1-1764.1-o
Conductor 1764.1
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 1764.1-o over \(\Q(\sqrt{13}) \)

Isogeny class 1764.1-o contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
1764.1-o1 \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -512 a + 1163\) , \( -11049 a + 25460\bigr] \)
1764.1-o2 \( \bigl[1\) , \( 1\) , \( a\) , \( 583 a - 1295\) , \( -9769 a + 22455\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph