Properties

Base field \(\Q(\sqrt{13}) \)
Label 2.2.13.1-23.1-a
Conductor 23.1
Rank \( 0 \)

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 23.1-a over \(\Q(\sqrt{13}) \)

Isogeny class 23.1-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
23.1-a1 \( \bigl[a\) , \( a\) , \( 0\) , \( a + 1\) , \( 0\bigr] \)
23.1-a2 \( \bigl[a\) , \( a\) , \( 0\) , \( -4 a - 4\) , \( -13 a - 18\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph