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

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-52.1-m
• Conductor: 52.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
52.1-m1	\( \bigl[a\) , \( 0\) , \( 0\) , \( -54 a + 253\) , \( -101 a + 462\bigr] \)
52.1-m2	\( \bigl[a\) , \( 0\) , \( 0\) , \( 706 a - 3187\) , \( 23075 a - 104546\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph