Elliptic curve isogeny class 9.2-b over number field \(\Q(\sqrt{97}) \)

• Base field: \(\Q(\sqrt{97}) \)
• Label: 2.2.97.1-9.2-b
• Conductor: 9.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{97}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 24 \); class number \(1\).

Elliptic curves in class 9.2-b over \(\Q(\sqrt{97}) \)

Isogeny class 9.2-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
9.2-b1	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 5\) , \( -a - 9\bigr] \)
9.2-b2	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -415172 a - 1836890\) , \( 288105428 a + 1274701983\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph