Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-49152.1-b
Conductor 49152.1
Rank \( 2 \)

Related objects

Learn more about

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

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

Elliptic curves in class 49152.1-b over \(\Q(\sqrt{-3}) \)

Isogeny class 49152.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
49152.1-b1 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -7 a\) , \( 9\bigr] \)
49152.1-b2 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 3 a\) , \( 3\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph