Elliptic curve isogeny class 14.2-b over number field \(\Q(\sqrt{65}) \)

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-14.2-b
• Conductor: 14.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 14.2-b over \(\Q(\sqrt{65}) \)

Isogeny class 14.2-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
14.2-b1	\( \bigl[a\) , \( 1\) , \( 0\) , \( -5 a - 248\) , \( -411 a - 3168\bigr] \)
14.2-b2	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -3 a - 8\) , \( -9 a - 35\bigr] \)
14.2-b3	\( \bigl[a\) , \( 1\) , \( 0\) , \( -45 a - 168\) , \( -451 a - 1632\bigr] \)
14.2-b4	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -9585 a - 33838\) , \( -1037541 a - 3663697\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph