Properties

Base field \(\Q(\sqrt{14}) \)
Label 2.2.56.1-256.1-f
Conductor 256.1
Rank not recorded

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Base field \(\Q(\sqrt{14}) \)

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

Elliptic curves in class 256.1-f over \(\Q(\sqrt{14}) \)

Isogeny class 256.1-f contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
256.1-f1 \( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 1\bigr] \)
256.1-f2 \( \bigl[0\) , \( a\) , \( 0\) , \( 280 a - 1043\) , \( -4877 a + 18250\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph