Properties

Base field \(\Q(\sqrt{57}) \)
Label 2.2.57.1-57.1-b
Conductor 57.1
Rank \( 0 \)

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-b over \(\Q(\sqrt{57}) \)

Isogeny class 57.1-b contains only one elliptic curve.

Curve label Weierstrass Coefficients
57.1-b1 \( \bigl[0\) , \( a - 1\) , \( 1\) , \( 264 a - 1125\) , \( 4176 a - 17851\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph