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

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

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

Curve label	Weierstrass Coefficients
405.1-h1	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -29 a - 101\) , \( 313 a + 992\bigr] \)
405.1-h2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2238 a + 7077\) , \( -183106 a - 579032\bigr] \)
405.1-h3	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -1160 a - 3671\) , \( -32376 a - 102383\bigr] \)
405.1-h4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -606 a - 1923\) , \( 14466 a + 45752\bigr] \)

Rank

Rank: \( 1 \)

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