Elliptic curve isogeny class 50.3-a over number field \(\Q(\sqrt{209}) \)

• Base field: \(\Q(\sqrt{209}) \)
• Label: 2.2.209.1-50.3-a
• Conductor: 50.3
• Rank: \( 2 \)

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

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

Elliptic curves in class 50.3-a over \(\Q(\sqrt{209}) \)

Isogeny class 50.3-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
50.3-a1	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -a\) , \( 0\bigr] \)
50.3-a2	\( \bigl[a\) , \( a\) , \( a + 1\) , \( -7329 a + 56779\) , \( -2133698 a + 16490518\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph