Properties

Base field \(\Q(\sqrt{57}) \)
Label 2.2.57.1-256.1-g
Conductor 256.1
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 256.1-g over \(\Q(\sqrt{57}) \)

Isogeny class 256.1-g contains only one elliptic curve.

Curve label Weierstrass Coefficients
256.1-g1 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2823 a - 9239\) , \( 158029 a + 517529\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph