Elliptic curve isogeny class 98.1-a over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-98.1-a
• Conductor: 98.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 98.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 98.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
98.1-a1	\( \bigl[a\) , \( -1\) , \( a\) , \( -172\) , \( 873\bigr] \)
98.1-a2	\( \bigl[a\) , \( -1\) , \( a\) , \( -2\) , \( -1\bigr] \)
98.1-a3	\( \bigl[a\) , \( -1\) , \( a\) , \( 3\) , \( 5\bigr] \)
98.1-a4	\( \bigl[a\) , \( -1\) , \( a\) , \( -37\) , \( 69\bigr] \)
98.1-a5	\( \bigl[a\) , \( -1\) , \( a\) , \( -12\) , \( -13\bigr] \)
98.1-a6	\( \bigl[a\) , \( -1\) , \( a\) , \( -2732\) , \( 55145\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph