Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-19200.1-d
Conductor 19200.1
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 19200.1-d over \(\Q(\sqrt{-3}) \)

Isogeny class 19200.1-d contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
19200.1-d1 \( \bigl[0\) , \( a\) , \( 0\) , \( 3 a - 18\) , \( -9 a + 27\bigr] \)
19200.1-d2 \( \bigl[0\) , \( a\) , \( 0\) , \( 43 a - 58\) , \( 159 a - 117\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph