Elliptic curve isogeny class 100.1-c over number field \(\Q(\sqrt{65}) \)

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-100.1-c
• Conductor: 100.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 100.1-c over \(\Q(\sqrt{65}) \)

Isogeny class 100.1-c contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
100.1-c1	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 227818 a - 1032272\) , \( 119423852 a - 541124864\bigr] \)
100.1-c2	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 24939 a - 113001\) , \( -5149703 a + 23333959\bigr] \)
100.1-c3	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 943 a - 4272\) , \( 377227 a - 1709264\bigr] \)
100.1-c4	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -181461 a + 822224\) , \( 38009182 a - 172224511\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph