Elliptic curve isogeny class 121.1-b over number field \(\Q(\sqrt{65}) \)

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-121.1-b
• Conductor: 121.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 121.1-b over \(\Q(\sqrt{65}) \)

Isogeny class 121.1-b contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
121.1-b1	\( \bigl[0\) , \( -a - 1\) , \( a\) , \( -70382 a - 250245\) , \( -20366022 a - 71943939\bigr] \)
121.1-b2	\( \bigl[0\) , \( -a - 1\) , \( a\) , \( -92 a - 325\) , \( -1612 a - 5699\bigr] \)
121.1-b3	\( \bigl[0\) , \( -a - 1\) , \( a\) , \( -2 a - 5\) , \( 18 a + 61\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph