Elliptic curve isogeny class 10.4-b over number field \(\Q(\sqrt{209}) \)

• Base field: \(\Q(\sqrt{209}) \)
• Label: 2.2.209.1-10.4-b
• Conductor: 10.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 10.4-b over \(\Q(\sqrt{209}) \)

Isogeny class 10.4-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
10.4-b1	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 16\) , \( a - 10\bigr] \)
10.4-b2	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -12491186 a - 84045873\) , \( -61050477246 a - 410773016901\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph