Elliptic curve isogeny class 289.2-c over number field \(\Q(\sqrt{-43}) \)

• Base field: \(\Q(\sqrt{-43}) \)
• Label: 2.0.43.1-289.2-c
• Conductor: 289.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-43}) \)

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

Elliptic curves in class 289.2-c over \(\Q(\sqrt{-43}) \)

Isogeny class 289.2-c contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
289.2-c1	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -2 a + 2\) , \( -a + 5\bigr] \)
289.2-c2	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 3 a + 97\) , \( -76 a + 76\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph