Properties

Base field \(\Q(\sqrt{69}) \)
Label 2.2.69.1-15.1-a
Conductor 15.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{69}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 17 \); class number \(1\).

Elliptic curves in class 15.1-a over \(\Q(\sqrt{69}) \)

Isogeny class 15.1-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
15.1-a1 \( \bigl[0\) , \( 1\) , \( a + 1\) , \( 2 a - 9\) , \( -3 a + 6\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph