Properties

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

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

Curve label Weierstrass Coefficients
3072.1-bn1 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6 a + 13\) , \( -23 a + 39\bigr] \)
3072.1-bn2 \( \bigl[0\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \)
3072.1-bn3 \( \bigl[0\) , \( -1\) , \( 0\) , \( 10 a - 33\) , \( -50 a + 69\bigr] \)
3072.1-bn4 \( \bigl[0\) , \( -1\) , \( 0\) , \( -10 a - 33\) , \( 50 a + 69\bigr] \)

Rank

Rank: \( 2 \)

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