Elliptic curve isogeny class 196.1-c over number field \(\Q(\sqrt{65}) \)

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-196.1-c
• Conductor: 196.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 196.1-c over \(\Q(\sqrt{65}) \)

Isogeny class 196.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
196.1-c1	\( \bigl[a\) , \( -1\) , \( 0\) , \( 159108 a - 721128\) , \( 69487828 a - 314864756\bigr] \)
196.1-c2	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 240 a + 826\) , \( 28 a + 120\bigr] \)
196.1-c3	\( \bigl[a\) , \( -1\) , \( 0\) , \( 948 a - 4328\) , \( -2300 a + 10380\bigr] \)
196.1-c4	\( \bigl[a\) , \( -1\) , \( 0\) , \( 9908 a - 45288\) , \( 1088004 a - 4933492\bigr] \)
196.1-c5	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -241 a + 1067\) , \( -29 a + 149\bigr] \)
196.1-c6	\( \bigl[a\) , \( -1\) , \( 0\) , \( 4068 a - 24808\) , \( 2165556 a - 10017396\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph