Elliptic curve isogeny class 90.1-a over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-90.1-a
• Conductor: 90.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 90.1-a over \(\Q(\sqrt{10}) \)

Isogeny class 90.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
90.1-a1	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -18 a - 46\) , \( -56 a - 174\bigr] \)
90.1-a2	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -258 a - 846\) , \( -3960 a - 12654\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph