Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-21609.3-b
Conductor 21609.3
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{-3}) \)

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

Elliptic curves in class 21609.3-b over \(\Q(\sqrt{-3}) \)

Isogeny class 21609.3-b contains 2 curves linked by isogenies of degree 13.

Curve label Weierstrass Coefficients
21609.3-b1 \( \bigl[0\) , \( a + 1\) , \( 1\) , \( -8210 a - 13685\) , \( -646946 a - 543199\bigr] \)
21609.3-b2 \( \bigl[0\) , \( a + 1\) , \( 1\) , \( -20 a - 35\) , \( 64 a + 71\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph