Properties

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

Related objects

Learn more

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

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

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

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

Curve label Weierstrass Coefficients
21609.3-c1 \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 13686 a + 8211\) , \( 625050 a - 1176460\bigr] \)
21609.3-c2 \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 36 a + 21\) , \( -120 a + 170\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph