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

• Base field: \(\Q(\sqrt{209}) \)
• Label: 2.2.209.1-10.1-c
• Conductor: 10.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
10.1-c1	\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 3 a + 20\bigr] \)
10.1-c2	\( \bigl[1\) , \( 1\) , \( 1\) , \( 512138585 a - 3958020110\) , \( 13200346700953 a - 102017772594930\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph