Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-900.1-k
Conductor 900.1
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 900.1-k over \(\Q(\sqrt{21}) \)

Isogeny class 900.1-k contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
900.1-k1 \( \bigl[1\) , \( -1\) , \( 1\) , \( -8\) , \( 11\bigr] \)
900.1-k2 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -30 a + 84\) , \( 0\bigr] \)
900.1-k3 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 120 a - 336\) , \( 432 a - 1206\bigr] \)
900.1-k4 \( \bigl[1\) , \( -1\) , \( 1\) , \( -128\) , \( 587\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph