Properties

Base field \(\Q(\sqrt{14}) \)
Label 2.2.56.1-18.1-b
Conductor 18.1
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 18.1-b over \(\Q(\sqrt{14}) \)

Isogeny class 18.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
18.1-b1 \( \bigl[a + 1\) , \( -1\) , \( a\) , \( -a + 2\) , \( 38 a - 142\bigr] \)
18.1-b2 \( \bigl[a + 1\) , \( -1\) , \( a\) , \( 79 a - 298\) , \( 738 a - 2762\bigr] \)

Rank

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Isogeny matrix

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

Isogeny graph