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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-92.1-a
• Conductor: 92.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
92.1-a1	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -a + 2\) , \( 0\bigr] \)
92.1-a2	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 74 a - 138\) , \( -412 a + 722\bigr] \)
92.1-a3	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 4 a - 8\) , \( 12 a - 22\bigr] \)
92.1-a4	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -a - 8\) , \( -10 a + 26\bigr] \)

Rank

Rank: \( 0 \)

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