Elliptic curve isogeny class 207.1-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-207.1-b
• Conductor: 207.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-11}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 3 \); class number \(1\).

Elliptic curves in class 207.1-b over \(\Q(\sqrt{-11}) \)

Isogeny class 207.1-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
207.1-b1	\( \bigl[a\) , \( 0\) , \( 1\) , \( -9 a\) , \( 11 a - 20\bigr] \)
207.1-b2	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -25 a + 7\) , \( -48 a + 106\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph