Properties

Base field \(\Q(\sqrt{14}) \)
Label 2.2.56.1-112.1-e
Conductor 112.1
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 112.1-e over \(\Q(\sqrt{14}) \)

Isogeny class 112.1-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
112.1-e1 \( \bigl[a\) , \( 1\) , \( 0\) , \( 150 a - 628\) , \( -1868 a + 7140\bigr] \)
112.1-e2 \( \bigl[a\) , \( 1\) , \( 0\) , \( 7\) , \( 4\bigr] \)
112.1-e3 \( \bigl[a\) , \( 1\) , \( 0\) , \( -8\) , \( -36\bigr] \)
112.1-e4 \( \bigl[a\) , \( 1\) , \( 0\) , \( 2\) , \( 0\bigr] \)
112.1-e5 \( \bigl[a\) , \( 1\) , \( 0\) , \( -68\) , \( 140\bigr] \)
112.1-e6 \( \bigl[a\) , \( 1\) , \( 0\) , \( -150 a - 628\) , \( 1868 a + 7140\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 8 & 4 & 2 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 8 & 4 & 1 & 2 & 4 & 8 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 2 & 4 & 4 & 2 & 1 & 2 \\ 4 & 8 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph