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

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

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

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

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

Curve label	Weierstrass Coefficients
90.1-c1	\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -6 a - 12\) , \( -12 a - 34\bigr] \)
90.1-c2	\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -66 a - 212\) , \( -560 a - 1794\bigr] \)