Elliptic curve isogeny class 52.1-d over number field \(\Q(\sqrt{65}) \)

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-52.1-d
• Conductor: 52.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 52.1-d over \(\Q(\sqrt{65}) \)

Isogeny class 52.1-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
52.1-d1	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -53 a - 180\) , \( 535 a + 1893\bigr] \)
52.1-d2	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 362 a + 1285\) , \( -2717 a - 9591\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph