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

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

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

Curve label	Weierstrass Coefficients
405.1-i1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -12 a + 37\) , \( -554 a + 1752\bigr] \)
405.1-i2	\( \bigl[1\) , \( -1\) , \( 1\) , \( 483 a - 1538\) , \( -10112 a + 31992\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph