Elliptic curve isogeny class 396.1-a over number field \(\Q(\sqrt{-43}) \)

• Base field: \(\Q(\sqrt{-43}) \)
• Label: 2.0.43.1-396.1-a
• Conductor: 396.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 396.1-a over \(\Q(\sqrt{-43}) \)

Isogeny class 396.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
396.1-a1	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -3 a + 7\) , \( 3\bigr] \)
396.1-a2	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -3 a + 17\) , \( 6 a - 11\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph