Elliptic curve isogeny class 484.1-b over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-484.1-b
• Conductor: 484.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 484.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 484.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
484.1-b1	\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( -78 a - 134\) , \( 474 a + 822\bigr] \)
484.1-b2	\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 2 a + 6\) , \( 4 a + 6\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph