Properties

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

Isogeny class 900.1-f contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
900.1-f1 \( \bigl[a\) , \( -1\) , \( 1\) , \( -41 a - 81\) , \( -765 a - 1339\bigr] \)
900.1-f2 \( \bigl[a\) , \( -1\) , \( 1\) , \( 4 a + 9\) , \( 27 a + 47\bigr] \)
900.1-f3 \( \bigl[a\) , \( -1\) , \( 1\) , \( -1361 a - 2721\) , \( -6525 a - 11419\bigr] \)
900.1-f4 \( \bigl[a\) , \( -1\) , \( 1\) , \( -206 a - 411\) , \( -2325 a - 4069\bigr] \)
900.1-f5 \( \bigl[a\) , \( -1\) , \( 1\) , \( -56 a - 111\) , \( 315 a + 551\bigr] \)
900.1-f6 \( \bigl[a\) , \( -1\) , \( 1\) , \( -1001 a - 2001\) , \( -28413 a - 49723\bigr] \)
900.1-f7 \( \bigl[a\) , \( -1\) , \( 1\) , \( -866 a - 1731\) , \( 22347 a + 39107\bigr] \)
900.1-f8 \( \bigl[a\) , \( -1\) , \( 1\) , \( -16001 a - 32001\) , \( -1804413 a - 3157723\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph