Elliptic curve isogeny class 450.3-j over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-450.3-j
• Conductor: 450.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 450.3-j over \(\Q(\sqrt{10}) \)

Isogeny class 450.3-j contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
450.3-j1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 128 a - 403\) , \( 1447 a - 4583\bigr] \)
450.3-j2	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 3 a - 3\) , \( 2 a - 3\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph