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

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-405.1-u
• 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-u over \(\Q(\sqrt{10}) \)

Isogeny class 405.1-u contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
405.1-u1	\( \bigl[a\) , \( -1\) , \( 0\) , \( 1971 a - 9540\) , \( -107750 a + 413885\bigr] \)
405.1-u2	\( \bigl[a\) , \( -1\) , \( 0\) , \( 351 a - 1080\) , \( 6982 a - 18475\bigr] \)
405.1-u3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -9 a\) , \( -2 a - 43\bigr] \)
405.1-u4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -9 a - 180\) , \( 250 a + 245\bigr] \)
405.1-u5	\( \bigl[a\) , \( -1\) , \( 0\) , \( -369 a - 2160\) , \( 9646 a + 41717\bigr] \)
405.1-u6	\( \bigl[a\) , \( -1\) , \( 0\) , \( -8469 a - 26460\) , \( 737026 a + 2371277\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 8 & 4 & 2 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 8 & 4 & 1 & 2 & 4 & 8 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 2 & 4 & 4 & 2 & 1 & 2 \\ 4 & 8 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph