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

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-52.1-h
• 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-h over \(\Q(\sqrt{65}) \)

Isogeny class 52.1-h contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
52.1-h1	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 386026 a - 1749144\) , \( 288323272 a - 1306429908\bigr] \)
52.1-h2	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 4876 a - 22104\) , \( -560288 a + 2538732\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph