Elliptic curve isogeny class 116.2-a over number field \(\Q(\sqrt{-5}) \)

• Base field: \(\Q(\sqrt{-5}) \)
• Label: 2.0.20.1-116.2-a
• Conductor: 116.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-5}) \)

Generator \(a\), with minimal polynomial \( x^{2} + 5 \); class number \(2\).

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 116.2-a over \(\Q(\sqrt{-5}) \)

Isogeny class 116.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
116.2-a1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -3 a - 4\) , \( -3 a + 3\bigr] \)
116.2-a2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2 a - 4\) , \( -2 a - 6\bigr] \)