Elliptic curve isogeny class 289.2-c over number field \(\Q(\sqrt{-67}) \)

• Base field: \(\Q(\sqrt{-67}) \)
• Label: 2.0.67.1-289.2-c
• Conductor: 289.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-67}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 17 \); class number \(1\).

Elliptic curves in class 289.2-c over \(\Q(\sqrt{-67}) \)

Isogeny class 289.2-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
289.2-c1	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a + 16\) , \( -a\bigr] \)
289.2-c2	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a + 11\) , \( 13\bigr] \)
289.2-c3	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 4 a + 11\) , \( 30\bigr] \)
289.2-c4	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -6 a - 69\) , \( 44 a + 428\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph