Elliptic curve isogeny class 324.1-d over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-324.1-d
• Conductor: 324.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 324.1-d over \(\Q(\sqrt{10}) \)

Isogeny class 324.1-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
324.1-d1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 1\bigr] \)
324.1-d2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -27\bigr] \)
324.1-d3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -15\) , \( 22\bigr] \)
324.1-d4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -135\) , \( -594\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph