Elliptic curve isogeny class 100.3-c over number field \(\Q(\sqrt{65}) \)

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-100.3-c
• Conductor: 100.3
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 100.3-c over \(\Q(\sqrt{65}) \)

Isogeny class 100.3-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
100.3-c1	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 24 a - 59\) , \( 68 a - 240\bigr] \)
100.3-c2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -6398 a + 28997\) , \( 1118144 a - 5066458\bigr] \)