Elliptic curve isogeny class 484.2-d over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-484.2-d
• Conductor: 484.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 484.2-d over \(\Q(\sqrt{3}) \)

Isogeny class 484.2-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
484.2-d1	\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( 637 a - 1214\) , \( 13085 a - 23088\bigr] \)
484.2-d2	\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -33 a + 56\) , \( 53 a - 94\bigr] \)