Elliptic curve isogeny class 49.1-a over number field \(\Q(\sqrt{-10}) \)

• Base field: \(\Q(\sqrt{-10}) \)
• Label: 2.0.40.1-49.1-a
• Conductor: 49.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-10}) \)

Generator \(a\), with minimal polynomial \( x^{2} + 10 \); class number \(2\).

Elliptic curves in class 49.1-a over \(\Q(\sqrt{-10}) \)

Isogeny class 49.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
49.1-a1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a + 2\) , \( -2 a - 24\bigr] \)
49.1-a2	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( a + 7\) , \( -a + 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph