Elliptic curve isogeny class 50.5-k over number field \(\Q(\sqrt{209}) \)

• Base field: \(\Q(\sqrt{209}) \)
• Label: 2.2.209.1-50.5-k
• Conductor: 50.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 50.5-k over \(\Q(\sqrt{209}) \)

Isogeny class 50.5-k contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
50.5-k1	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -1243 a - 8318\) , \( 60360 a + 406216\bigr] \)
50.5-k2	\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 141381205 a + 951271648\) , \( -5674189094062 a - 38178305523752\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph