Elliptic curve isogeny class 441.2-a over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-441.2-a
• Conductor: 441.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 441.2-a over \(\Q(\sqrt{10}) \)

Isogeny class 441.2-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
441.2-a1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -474 a - 1539\) , \( -9615 a - 30331\bigr] \)
441.2-a2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a + 21\) , \( 9 a + 29\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph