Elliptic curve isogeny class 225.1-n over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-225.1-n
• Conductor: 225.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 225.1-n over \(\Q(\sqrt{10}) \)

Isogeny class 225.1-n contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
225.1-n1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a - 5\) , \( 5 a - 20\bigr] \)
225.1-n2	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -2 a - 3\) , \( -a - 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph