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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-54.1-c
• 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-c over \(\Q(\sqrt{3}) \)

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

Curve label	Weierstrass Coefficients
54.1-c1	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 22 a - 41\) , \( -218 a + 377\bigr] \)
54.1-c2	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -3 a + 4\) , \( 7 a - 14\bigr] \)
54.1-c3	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 127 a - 221\) , \( 1000 a - 1734\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph