Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-300.1-h
Conductor 300.1
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 300.1-h over \(\Q(\sqrt{21}) \)

Isogeny class 300.1-h contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
300.1-h1 \( \bigl[a\) , \( 1\) , \( 1\) , \( 6 a - 16\) , \( -9 a + 26\bigr] \)
300.1-h2 \( \bigl[a\) , \( 1\) , \( 1\) , \( 96 a - 286\) , \( -765 a + 2150\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph