Elliptic curve isogeny class 162.1-b over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-162.1-b
• Conductor: 162.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 162.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 162.1-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
162.1-b1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \)
162.1-b2	\( \bigl[a\) , \( 0\) , \( a\) , \( -15\) , \( -30\bigr] \)
162.1-b3	\( \bigl[a\) , \( 0\) , \( a\) , \( 0\) , \( 0\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph