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

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-405.1-o
• Conductor: 405.1
• Rank: \( 0 \)

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

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

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

Isogeny class 405.1-o contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
405.1-o1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -114 a - 387\) , \( 2622 a + 8344\bigr] \)
405.1-o2	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 559 a + 1765\) , \( -22609 a - 71497\bigr] \)
405.1-o3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -4638 a - 14667\) , \( -254366 a - 804376\bigr] \)
405.1-o4	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -152 a - 485\) , \( 1732 a + 5476\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph