Elliptic curve isogeny class 20.1-b over number field \(\Q(\sqrt{11}) \)

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-20.1-b
• Conductor: 20.1
• Rank: \( 0 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - 11 \); class number \(1\).

Elliptic curves in class 20.1-b over \(\Q(\sqrt{11}) \)

Isogeny class 20.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
20.1-b1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -12 a + 46\) , \( -82 a + 269\bigr] \)
20.1-b2	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -5 a - 9\) , \( a + 8\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph