Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-441.1-g
Conductor 441.1
Rank \( 1 \)

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 441.1-g over \(\Q(\sqrt{21}) \)

Isogeny class 441.1-g contains 2 curves linked by isogenies of degree 13.

Curve label Weierstrass Coefficients
441.1-g1 \( \bigl[0\) , \( a + 1\) , \( 1\) , \( 2738 a - 8209\) , \( -128294 a + 352126\bigr] \)
441.1-g2 \( \bigl[0\) , \( a + 1\) , \( 1\) , \( 8 a - 19\) , \( 16 a - 44\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph