Properties

Base field \(\Q(\sqrt{57}) \)
Label 2.2.57.1-228.1-r
Conductor 228.1
Rank \( 1 \)

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Base field \(\Q(\sqrt{57}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 14 \); class number \(1\).

Elliptic curves in class 228.1-r over \(\Q(\sqrt{57}) \)

Isogeny class 228.1-r contains only one elliptic curve.

Curve label Weierstrass Coefficients
228.1-r1 \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 9 a - 29\) , \( -181 a + 779\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph