Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-768.1-b
Conductor 768.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{21}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 5 \); class number \(1\).

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 768.1-b over \(\Q(\sqrt{21}) \)

Isogeny class 768.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
768.1-b1 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -8 a - 13\) , \( -14 a - 26\bigr] \)
768.1-b2 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -128 a - 228\) , \( -1116 a - 2000\bigr] \)