Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-1176.1-h
Conductor 1176.1
Rank \( 1 \)

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Base field \(\Q(\sqrt{3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 1176.1-h over \(\Q(\sqrt{3}) \)

Isogeny class 1176.1-h contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
1176.1-h1 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -48 a + 84\) , \( -90 a + 156\bigr] \)
1176.1-h2 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 12 a - 21\) , \( 0\bigr] \)
1176.1-h3 \( \bigl[0\) , \( 1\) , \( 0\) , \( -7\) , \( -10\bigr] \)
1176.1-h4 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 152 a - 266\) , \( -1260 a + 2184\bigr] \)

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