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

• Base field: \(\Q(\sqrt{209}) \)
• Label: 2.2.209.1-50.3-f
• Conductor: 50.3
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
50.3-f1	\( \bigl[1\) , \( -a\) , \( 0\) , \( 5 a - 20\) , \( 24 a - 201\bigr] \)
50.3-f2	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -3817379 a - 25684905\) , \( -10751246830 a - 72338862782\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph