Elliptic curve isogeny class 8.2-a over number field \(\Q(\sqrt{97}) \)

• Base field: \(\Q(\sqrt{97}) \)
• Label: 2.2.97.1-8.2-a
• Conductor: 8.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 8.2-a over \(\Q(\sqrt{97}) \)

Isogeny class 8.2-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
8.2-a1	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 348 a - 1845\) , \( 9280 a - 50285\bigr] \)
8.2-a2	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 4 a + 23\) , \( 6 a + 29\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph