Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-784.1-c
Conductor 784.1
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 784.1-c over \(\Q(\sqrt{21}) \)

Isogeny class 784.1-c contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
784.1-c1 \( \bigl[0\) , \( -a\) , \( 0\) , \( 12 a - 31\) , \( 13 a - 37\bigr] \)
784.1-c2 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -712 a - 1279\) , \( -16113 a - 28864\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph