Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-49152.1-t
Conductor 49152.1
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 49152.1-t over \(\Q(\sqrt{-3}) \)

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

Curve label Weierstrass Coefficients
49152.1-t1 \( \bigl[0\) , \( 1\) , \( 0\) , \( 8 a - 5\) , \( -8 a + 3\bigr] \)
49152.1-t2 \( \bigl[0\) , \( 1\) , \( 0\) , \( -2 a\) , \( -2 a\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph