Properties

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

Isogeny class 112.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
112.1-a1 \( \bigl[a\) , \( 0\) , \( a\) , \( -685\) , \( -7674\bigr] \)
112.1-a2 \( \bigl[a\) , \( 0\) , \( a\) , \( -5\) , \( -2\bigr] \)
112.1-a3 \( \bigl[a\) , \( 0\) , \( a\) , \( 15\) , \( -30\bigr] \)
112.1-a4 \( \bigl[a\) , \( 0\) , \( a\) , \( -145\) , \( -702\bigr] \)
112.1-a5 \( \bigl[a\) , \( 0\) , \( a\) , \( -45\) , \( 54\bigr] \)
112.1-a6 \( \bigl[a\) , \( 0\) , \( a\) , \( -10925\) , \( -452090\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph