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

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-100.3-a
• 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

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph

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

Isogeny class 100.3-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
100.3-a1	\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( -58 a - 198\) , \( 369 a + 1298\bigr] \)