Elliptic curve isogeny class 360.1-e over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-360.1-e
• Conductor: 360.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 360.1-e over \(\Q(\sqrt{10}) \)

Isogeny class 360.1-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
360.1-e1	\( \bigl[a\) , \( 1\) , \( a\) , \( -21\) , \( -321\bigr] \)
360.1-e2	\( \bigl[a\) , \( 1\) , \( a\) , \( 19\) , \( 29\bigr] \)
360.1-e3	\( \bigl[a\) , \( 1\) , \( a\) , \( -6\) , \( -6\bigr] \)
360.1-e4	\( \bigl[a\) , \( 1\) , \( a\) , \( -51\) , \( -195\bigr] \)
360.1-e5	\( \bigl[0\) , \( -1\) , \( 0\) , \( -61\) , \( 205\bigr] \)
360.1-e6	\( \bigl[a\) , \( 1\) , \( a\) , \( -801\) , \( -9645\bigr] \)

Rank

Rank: \( 2 \)

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