Elliptic curve isogeny class 98.1-d over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-98.1-d
• Conductor: 98.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{6}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 6 \); class number \(1\).

Elliptic curves in class 98.1-d over \(\Q(\sqrt{6}) \)

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

Curve label	Weierstrass Coefficients
98.1-d1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 3411 a - 8354\) , \( -169592 a + 415414\bigr] \)
98.1-d2	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 11 a - 24\) , \( 60 a - 146\bigr] \)
98.1-d3	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 89 a + 221\) , \( 1228 a + 3009\bigr] \)
98.1-d4	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -711 a - 1739\) , \( 13100 a + 32089\bigr] \)
98.1-d5	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -211 a - 514\) , \( -2636 a - 6456\bigr] \)
98.1-d6	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -54611 a - 133794\) , \( 10864248 a + 26611894\bigr] \)

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