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

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-100.1-j
• 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-j over \(\Q(\sqrt{65}) \)

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

Curve label	Weierstrass Coefficients
100.1-j1	\( \bigl[a\) , \( -1\) , \( a\) , \( 867 a - 3968\) , \( -27959 a + 126716\bigr] \)
100.1-j2	\( \bigl[a\) , \( -1\) , \( a\) , \( -8 a + 32\) , \( 71 a - 324\bigr] \)