Elliptic curve isogeny class 64.1-b over number field \(\Q(\sqrt{11}) \)

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-64.1-b
• Conductor: 64.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 64.1-b over \(\Q(\sqrt{11}) \)

Isogeny class 64.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
64.1-b1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)
64.1-b2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 60 a + 199\) , \( 0\bigr] \)
64.1-b3	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -163 a - 542\) , \( -2531 a - 8396\bigr] \)
64.1-b4	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -162 a - 536\) , \( 1659 a + 5502\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph