Elliptic curve isogeny class 10.1-b over number field \(\Q(\sqrt{65}) \)

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-10.1-b
• Conductor: 10.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{65}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 16 \); class number \(2\).

Elliptic curves in class 10.1-b over \(\Q(\sqrt{65}) \)

Isogeny class 10.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
10.1-b1	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -72 a - 256\) , \( -998 a - 3528\bigr] \)
10.1-b2	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 3 a + 9\) , \( 2 a + 3\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph