Properties

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

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

Curve label Weierstrass Coefficients
10.2-d1 \( \bigl[1\) , \( a - 1\) , \( 0\) , \( 20 a - 72\) , \( -128 a + 480\bigr] \)
10.2-d2 \( \bigl[1\) , \( a - 1\) , \( 0\) , \( 3\) , \( 1\bigr] \)

Rank

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Isogeny matrix

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

Isogeny graph