Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-1344.1-a
Conductor 1344.1
Rank \( 0 \)

Related objects

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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 1344.1-a over \(\Q(\sqrt{21}) \)

Isogeny class 1344.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
1344.1-a1 \( \bigl[0\) , \( 1\) , \( 0\) , \( 25 a - 72\) , \( 111 a - 328\bigr] \)
1344.1-a2 \( \bigl[0\) , \( 1\) , \( 0\) , \( 48\) , \( 48\bigr] \)
1344.1-a3 \( \bigl[0\) , \( 1\) , \( 0\) , \( -12\) , \( 0\bigr] \)
1344.1-a4 \( \bigl[0\) , \( 1\) , \( 0\) , \( -7\) , \( -10\bigr] \)
1344.1-a5 \( \bigl[0\) , \( 1\) , \( 0\) , \( -152\) , \( 672\bigr] \)
1344.1-a6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -25 a - 47\) , \( -111 a - 217\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph