Elliptic curve isogeny class 72.1-e over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-72.1-e
• Conductor: 72.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 72.1-e over \(\Q(\sqrt{10}) \)

Isogeny class 72.1-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
72.1-e1	\( \bigl[a\) , \( 0\) , \( 0\) , \( 6\) , \( -18\bigr] \)
72.1-e2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( 3\bigr] \)
72.1-e3	\( \bigl[a\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)
72.1-e4	\( \bigl[a\) , \( 0\) , \( 0\) , \( -4\) , \( -10\bigr] \)
72.1-e5	\( \bigl[a\) , \( 0\) , \( 0\) , \( -14\) , \( 12\bigr] \)
72.1-e6	\( \bigl[a\) , \( 0\) , \( 0\) , \( -94\) , \( -442\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph