Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-1536.1-d
Conductor 1536.1
Rank \( 0 \)

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 1536.1-d over \(\Q(\sqrt{3}) \)

Isogeny class 1536.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
1536.1-d1 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 12 a - 24\) , \( -108 a + 180\bigr] \)
1536.1-d2 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 59058 a - 102289\) , \( -10267037 a + 17783029\bigr] \)
1536.1-d3 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 3693 a - 6394\) , \( -159632 a + 276490\bigr] \)
1536.1-d4 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4758 a - 8239\) , \( -59237 a + 102601\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph