Elliptic curve isogeny class 65.1-b over number field \(\Q(\sqrt{65}) \)

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-65.1-b
• Conductor: 65.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 65.1-b over \(\Q(\sqrt{65}) \)

Isogeny class 65.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
65.1-b1	\( \bigl[a\) , \( 0\) , \( a\) , \( 36 a + 125\) , \( 113 a + 398\bigr] \)
65.1-b2	\( \bigl[a\) , \( 0\) , \( a\) , \( -9 a - 35\) , \( -9 a - 34\bigr] \)
65.1-b3	\( \bigl[1\) , \( 1\) , \( 0\) , \( -1125 a - 3972\) , \( -41459 a - 146397\bigr] \)
65.1-b4	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -7 a - 20\) , \( 9 a + 29\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph