Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-47.1-b
Conductor 47.1
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 47.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 47.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
47.1-b1 \( \bigl[1\) , \( a\) , \( 1\) , \( a - 1\) , \( 0\bigr] \)
47.1-b2 \( \bigl[1\) , \( a\) , \( 1\) , \( 6 a - 11\) , \( -14 a + 24\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph