Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-1800.1-b
Conductor 1800.1
Rank \( 0 \)

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

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

Elliptic curves in class 1800.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 1800.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
1800.1-b1 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -3 a - 3\) , \( -36 a - 63\bigr] \)
1800.1-b2 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -123 a - 213\) , \( -1086 a - 1881\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph