Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-54.1-b
Conductor 54.1
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 54.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 54.1-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
54.1-b1 \( \bigl[a\) , \( 0\) , \( a + 1\) , \( 22 a - 42\) , \( 217 a - 379\bigr] \)
54.1-b2 \( \bigl[a\) , \( 0\) , \( a + 1\) , \( -3 a + 3\) , \( -8 a + 12\bigr] \)
54.1-b3 \( \bigl[a\) , \( 0\) , \( a + 1\) , \( 127 a - 222\) , \( -1001 a + 1732\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph