Elliptic curve isogeny class 80.1-d over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-80.1-d
• Conductor: 80.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 80.1-d over \(\Q(\sqrt{10}) \)

Isogeny class 80.1-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
80.1-d1	\( \bigl[a\) , \( 0\) , \( 0\) , \( -7\) , \( 9\bigr] \)
80.1-d2	\( \bigl[a\) , \( 0\) , \( 0\) , \( 3\) , \( 1\bigr] \)
80.1-d3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -5\) , \( -5\bigr] \)
80.1-d4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -165\) , \( 763\bigr] \)

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