Elliptic curve isogeny class 6.1-a over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-6.1-a
• Conductor: 6.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 6.1-a over \(\Q(\sqrt{10}) \)

Isogeny class 6.1-a contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
6.1-a1	\( \bigl[a\) , \( a\) , \( 0\) , \( 1263 a - 8032\) , \( 62956 a - 305877\bigr] \)
6.1-a2	\( \bigl[a\) , \( a\) , \( 0\) , \( 3 a + 8\) , \( 4 a + 3\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph