Elliptic curve isogeny class 11.1-b over number field \(\Q(\sqrt{209}) \)

• Base field: \(\Q(\sqrt{209}) \)
• Label: 2.2.209.1-11.1-b
• Conductor: 11.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 11.1-b over \(\Q(\sqrt{209}) \)

Isogeny class 11.1-b contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
11.1-b1	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 4688891060561 a - 36237701385816\) , \( -14859019779017908422 a + 114836688394705117771\bigr] \)
11.1-b2	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -6195627759 a - 41686761846\) , \( 1292706345403712 a + 8697866248261405\bigr] \)
11.1-b3	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 199858961 a - 1544593196\) , \( 9820121401118 a - 75893984805809\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph