Properties

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

Isogeny class 3072.1-cd contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
3072.1-cd1 \( \bigl[0\) , \( -1\) , \( 0\) , \( 122 a - 225\) , \( -1074 a + 1797\bigr] \)
3072.1-cd2 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 1500096 a - 2598240\) , \( 1316558104 a - 2280345528\bigr] \)
3072.1-cd3 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 95576 a - 165540\) , \( 19749120 a - 34206480\bigr] \)
3072.1-cd4 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -322420 a + 558448\) , \( 571215336 a - 989373984\bigr] \)
3072.1-cd5 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 1612 a - 2792\) , \( -39276 a + 68028\bigr] \)
3072.1-cd6 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -3308 a + 5728\) , \( -220380 a + 381708\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph