Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-4056.1-e
Conductor 4056.1
Rank \( 1 \)

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 4056.1-e over \(\Q(\sqrt{3}) \)

Isogeny class 4056.1-e contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
4056.1-e1 \( \bigl[0\) , \( 1\) , \( 0\) , \( 5\) , \( 14\bigr] \)
4056.1-e2 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 60 a - 105\) , \( -270 a + 468\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph