Elliptic curve isogeny class 54.1-d over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-54.1-d
• Conductor: 54.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 54.1-d over \(\Q(\sqrt{3}) \)

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

Curve label	Weierstrass Coefficients
54.1-d1	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -128 a - 222\) , \( 1000 a + 1732\bigr] \)
54.1-d2	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -23 a - 42\) , \( -218 a - 379\bigr] \)
54.1-d3	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 2 a + 3\) , \( 7 a + 12\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph