Elliptic curve isogeny class 2.2-b over number field \(\Q(\sqrt{209}) \)

• Base field: \(\Q(\sqrt{209}) \)
• Label: 2.2.209.1-2.2-b
• Conductor: 2.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 2.2-b over \(\Q(\sqrt{209}) \)

Isogeny class 2.2-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
2.2-b1	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 166348 a - 1285588\) , \( 101485499 a - 784322149\bigr] \)
2.2-b2	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 6449267 a + 43393366\) , \( 1546707281 a + 10406890251\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph