Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-324.1-d
Conductor 324.1
Rank not recorded

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Base field \(\Q(\sqrt{21}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 5 \); class number \(1\).

Elliptic curves in class 324.1-d over \(\Q(\sqrt{21}) \)

Isogeny class 324.1-d contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
324.1-d1 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 15 a - 42\) , \( 72 a - 201\bigr] \)
324.1-d2 \( \bigl[1\) , \( -1\) , \( 1\) , \( -14\) , \( 29\bigr] \)
324.1-d3 \( \bigl[1\) , \( -1\) , \( 1\) , \( 1\) , \( -1\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph