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

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-225.1-k
• Conductor: 225.1
• Rank: \( 1 \)

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

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

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

Isogeny class 225.1-k contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
225.1-k1	\( \bigl[0\) , \( -a\) , \( 1\) , \( -643 a - 2030\) , \( 16466 a + 52071\bigr] \)
225.1-k2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 12 a + 30\) , \( 198 a + 630\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph