Elliptic curve isogeny class 98.1-b over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-98.1-b
• Conductor: 98.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{10}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 10 \); class number \(2\).

Elliptic curves in class 98.1-b over \(\Q(\sqrt{10}) \)

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

Curve label	Weierstrass Coefficients
98.1-b1	\( \bigl[a\) , \( 1\) , \( a\) , \( -683\) , \( -7673\bigr] \)
98.1-b2	\( \bigl[a\) , \( 1\) , \( a\) , \( -3\) , \( -1\bigr] \)
98.1-b3	\( \bigl[a\) , \( 1\) , \( a\) , \( 17\) , \( -29\bigr] \)
98.1-b4	\( \bigl[a\) , \( 1\) , \( a\) , \( -143\) , \( -701\bigr] \)
98.1-b5	\( \bigl[a\) , \( 1\) , \( a\) , \( -43\) , \( 55\bigr] \)
98.1-b6	\( \bigl[a\) , \( 1\) , \( a\) , \( -10923\) , \( -452089\bigr] \)

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