Properties

Base field \(\Q(\sqrt{13}) \)
Label 2.2.13.1-361.1-a
Conductor 361.1
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 361.1-a over \(\Q(\sqrt{13}) \)

Isogeny class 361.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
361.1-a1 \( \bigl[0\) , \( 1\) , \( 1\) , \( -769\) , \( -8470\bigr] \)
361.1-a2 \( \bigl[0\) , \( 1\) , \( 1\) , \( -9\) , \( -15\bigr] \)
361.1-a3 \( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( 0\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph