Properties

Base field \(\Q(\sqrt{14}) \)
Label 2.2.56.1-10.2-a
Conductor 10.2
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 10.2-a over \(\Q(\sqrt{14}) \)

Isogeny class 10.2-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
10.2-a1 \( \bigl[1\) , \( 0\) , \( 1\) , \( -18 a - 68\) , \( -814 a - 3046\bigr] \)
10.2-a2 \( \bigl[1\) , \( 0\) , \( 1\) , \( 2 a + 7\) , \( 30 a + 112\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph