Elliptic curve isogeny class 324.4-c over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-324.4-c
• Conductor: 324.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 324.4-c over \(\Q(\sqrt{10}) \)

Isogeny class 324.4-c contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
324.4-c1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 5578 a - 17638\) , \( 718126 a - 2270914\bigr] \)
324.4-c2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -582 a + 1842\) , \( -19130 a + 60494\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph