Properties

Base field \(\Q(\sqrt{57}) \)
Label 2.2.57.1-57.1-h
Conductor 57.1
Rank \( 1 \)

Related objects

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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 57.1-h over \(\Q(\sqrt{57}) \)

Isogeny class 57.1-h contains only one elliptic curve.

Curve label Weierstrass Coefficients
57.1-h1 \( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -38 a + 166\) , \( 9 a - 40\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph