Properties

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

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

Curve label Weierstrass Coefficients
19200.1-b1 \( \bigl[0\) , \( a\) , \( 0\) , \( 58 a - 43\) , \( -159 a + 42\bigr] \)
19200.1-b2 \( \bigl[0\) , \( a\) , \( 0\) , \( 18 a - 3\) , \( 9 a + 18\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph