Elliptic curve isogeny class 405.3-a over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-405.3-a
• Conductor: 405.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 405.3-a over \(\Q(\sqrt{10}) \)

Isogeny class 405.3-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
405.3-a1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -50 a - 151\) , \( 299 a + 941\bigr] \)
405.3-a2	\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( a - 1\) , \( -3\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph