Properties

Base field \(\Q(\sqrt{14}) \)
Label 2.2.56.1-56.1-c
Conductor 56.1
Rank \( 1 \)

Related objects

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

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

Elliptic curves in class 56.1-c over \(\Q(\sqrt{14}) \)

Isogeny class 56.1-c contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
56.1-c1 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 7 a - 33\) , \( 1856 a - 6948\bigr] \)
56.1-c2 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 1207 a - 4523\) , \( 47106 a - 176258\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph