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

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-450.3-v
• 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-v over \(\Q(\sqrt{10}) \)

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

Curve label	Weierstrass Coefficients
450.3-v1	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 251 a - 802\) , \( -3608 a + 11406\bigr] \)
450.3-v2	\( \bigl[a\) , \( a\) , \( 0\) , \( 5 a + 80\) , \( -40 a + 275\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph