Elliptic curve isogeny class 50.6-d over number field \(\Q(\sqrt{209}) \)

• Base field: \(\Q(\sqrt{209}) \)
• Label: 2.2.209.1-50.6-d
• Conductor: 50.6
• Rank: \( 1 \)

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

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

Elliptic curves in class 50.6-d over \(\Q(\sqrt{209}) \)

Isogeny class 50.6-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
50.6-d1	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -197 a - 1316\) , \( -3768 a - 25359\bigr] \)
50.6-d2	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 93108 a - 719551\) , \( -1558031245928 a + 12041113839211\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph