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

• Base field: \(\Q(\sqrt{209}) \)
• Label: 2.2.209.1-50.3-g
• Conductor: 50.3
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
50.3-g1	\( \bigl[a\) , \( a\) , \( 1\) , \( 557954489 a - 4312104315\) , \( -19506746796820 a + 150756256928227\bigr] \)
50.3-g2	\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 48081 a + 323494\) , \( -615506 a - 4141387\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph