Elliptic curve isogeny class 8.1-a over number field \(\Q(\sqrt{97}) \)

• Base field: \(\Q(\sqrt{97}) \)
• Label: 2.2.97.1-8.1-a
• Conductor: 8.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 8.1-a over \(\Q(\sqrt{97}) \)

Isogeny class 8.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
8.1-a1	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -347 a - 1522\) , \( -8933 a - 39507\bigr] \)
8.1-a2	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -3 a + 2\) , \( -3 a + 9\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph