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

• Base field: \(\Q(\sqrt{-43}) \)
• Label: 2.0.43.1-289.2-b
• 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-b over \(\Q(\sqrt{-43}) \)

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

Curve label	Weierstrass Coefficients
289.2-b1	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -3 a - 6\) , \( 8\bigr] \)
289.2-b2	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -8 a + 94\) , \( 175 a - 41\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph