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

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-14.2-c
• Conductor: 14.2
• 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 14.2-c over \(\Q(\sqrt{65}) \)

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

Curve label	Weierstrass Coefficients
14.2-c1	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 133 a - 600\) , \( 1801 a - 8174\bigr] \)
14.2-c2	\( \bigl[a\) , \( a\) , \( a\) , \( 1649 a - 7451\) , \( 77153 a - 349562\bigr] \)
14.2-c3	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 8 a - 35\) , \( 33 a - 158\bigr] \)
14.2-c4	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( a - 64\) , \( -43 a - 324\bigr] \)