Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-100.1-a
Conductor 100.1
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 100.1-a over \(\Q(\sqrt{21}) \)

Isogeny class 100.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
100.1-a1 \( \bigl[a\) , \( a - 1\) , \( 1\) , \( a\) , \( 1\bigr] \)
100.1-a2 \( \bigl[a\) , \( a - 1\) , \( 1\) , \( 11 a - 30\) , \( 24 a - 67\bigr] \)
100.1-a3 \( \bigl[a\) , \( a - 1\) , \( 1\) , \( 36 a - 110\) , \( -222 a + 623\bigr] \)
100.1-a4 \( \bigl[a\) , \( a - 1\) , \( 1\) , \( -4 a - 190\) , \( -14 a + 911\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph