Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-3072.1-bp
Conductor 3072.1
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 3072.1-bp over \(\Q(\sqrt{3}) \)

Isogeny class 3072.1-bp contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
3072.1-bp1 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 84 a - 143\) , \( 488 a - 846\bigr] \)
3072.1-bp2 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4\) , \( -4 a + 4\bigr] \)
3072.1-bp3 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 20 a - 64\) , \( -124 a + 268\bigr] \)
3072.1-bp4 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -20 a - 24\) , \( -60 a - 84\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph