Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-625.1-q
Conductor 625.1
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 625.1-q over \(\Q(\sqrt{21}) \)

Isogeny class 625.1-q contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
625.1-q1 \( \bigl[0\) , \( -a - 1\) , \( a\) , \( a + 2\) , \( -25 a + 57\bigr] \)
625.1-q2 \( \bigl[0\) , \( a + 1\) , \( a\) , \( a + 2\) , \( 212 a + 378\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph