Elliptic curve isogeny class 405.1-v over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-405.1-v
• Conductor: 405.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 405.1-v over \(\Q(\sqrt{10}) \)

Isogeny class 405.1-v contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
405.1-v1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 3006 a - 9507\) , \( 226442 a - 716076\bigr] \)
405.1-v2	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 3343 a - 10580\) , \( 188817 a - 597099\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph