Properties

Base field \(\Q(\sqrt{14}) \)
Label 2.2.56.1-32.1-d
Conductor 32.1
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 32.1-d over \(\Q(\sqrt{14}) \)

Isogeny class 32.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
32.1-d1 \( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)
32.1-d2 \( \bigl[0\) , \( 0\) , \( 0\) , \( 120 a + 449\) , \( 0\bigr] \)
32.1-d3 \( \bigl[a\) , \( 1\) , \( 0\) , \( -330 a - 1228\) , \( -6788 a - 25395\bigr] \)
32.1-d4 \( \bigl[a\) , \( 1\) , \( a\) , \( -330 a - 1235\) , \( 5798 a + 21694\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph