Elliptic curve isogeny class 361.3-b over number field \(\Q(\sqrt{11}) \)

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-361.3-b
• Conductor: 361.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 361.3-b over \(\Q(\sqrt{11}) \)

Isogeny class 361.3-b contains 2 curves linked by isogenies of degree 11.

Curve label	Weierstrass Coefficients
361.3-b1	\( \bigl[0\) , \( a - 1\) , \( a\) , \( 106 a - 350\) , \( 968 a - 3213\bigr] \)
361.3-b2	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 106 a - 350\) , \( -968 a + 3210\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph