Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-4096.1-g
Conductor 4096.1
Rank \( 2 \)

Related objects

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

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 4096.1-g over \(\Q(\sqrt{3}) \)

Isogeny class 4096.1-g contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
4096.1-g1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 14 a - 22\) , \( 28 a - 48\bigr] \)
4096.1-g2 \( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( 1\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph