Elliptic curve isogeny class 10.1-b over number field \(\Q(\sqrt{209}) \)

• Base field: \(\Q(\sqrt{209}) \)
• Label: 2.2.209.1-10.1-b
• Conductor: 10.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{209}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 52 \); class number \(1\).

Elliptic curves in class 10.1-b over \(\Q(\sqrt{209}) \)

Isogeny class 10.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
10.1-b1	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 12491185 a - 96537059\) , \( 61050477245 a - 471823494147\bigr] \)
10.1-b2	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -a + 17\) , \( -2 a - 8\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph