Elliptic curve isogeny class 92.1-b over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-92.1-b
• Conductor: 92.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 92.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 92.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
92.1-b1	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -a - 1\) , \( -a\bigr] \)
92.1-b2	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 74 a - 141\) , \( 486 a - 862\bigr] \)
92.1-b3	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 4 a - 11\) , \( -8 a + 12\bigr] \)
92.1-b4	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -a - 11\) , \( 9 a - 36\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph