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

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-100.1-a
• Conductor: 100.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

Isogeny class 100.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
100.1-a1	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 3964 a - 17953\) , \( -280263 a + 1269909\bigr] \)
100.1-a2	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -36 a + 172\) , \( 772 a - 3496\bigr] \)