Elliptic curve isogeny class 25.2-a over number field \(\Q(\sqrt{209}) \)

• Base field: \(\Q(\sqrt{209}) \)
• Label: 2.2.209.1-25.2-a
• Conductor: 25.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 25.2-a over \(\Q(\sqrt{209}) \)

Isogeny class 25.2-a contains 2 curves linked by isogenies of degree 19.

Curve label	Weierstrass Coefficients
25.2-a1	\( \bigl[0\) , \( 0\) , \( 1\) , \( 43199424 a - 333863126\) , \( 415934860788 a - 3214517694381\bigr] \)
25.2-a2	\( \bigl[0\) , \( 0\) , \( 1\) , \( -96 a - 646\) , \( -1378 a - 9272\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 19 \\ 19 & 1 \end{array}\right)\)

Isogeny graph