Elliptic curve isogeny class 1.1-b over number field \(\Q(\sqrt{165}) \)

• Base field: \(\Q(\sqrt{165}) \)
• Label: 2.2.165.1-1.1-b
• Conductor: 1.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{165}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 41 \); class number \(2\).

Elliptic curves in class 1.1-b over \(\Q(\sqrt{165}) \)

Isogeny class 1.1-b contains 2 curves linked by isogenies of degree 11.

Curve label	Weierstrass Coefficients
1.1-b1	\( \bigl[0\) , \( 0\) , \( 1\) , \( 1008 a - 6978\) , \( 45297 a - 313574\bigr] \)
1.1-b2	\( \bigl[0\) , \( 0\) , \( 1\) , \( 6 a - 42\) , \( -21 a + 145\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph