Elliptic curve isogeny class 14.3-c over number field \(\Q(\sqrt{65}) \)

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-14.3-c
• Conductor: 14.3
• Rank: \( 0 \)

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

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

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

Elliptic curves in class 14.3-c over \(\Q(\sqrt{65}) \)

Isogeny class 14.3-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
14.3-c1	\( \bigl[a\) , \( 1\) , \( a\) , \( -7 a - 32\) , \( -42 a - 160\bigr] \)
14.3-c2	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 2110 a - 9536\) , \( 104711 a - 474436\bigr] \)
14.3-c3	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -7 a - 27\) , \( -42 a - 151\bigr] \)
14.3-c4	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -132 a - 467\) , \( -1935 a - 6839\bigr] \)