Elliptic curve isogeny class 324.3-b over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-324.3-b
• Conductor: 324.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 324.3-b over \(\Q(\sqrt{10}) \)

Isogeny class 324.3-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
324.3-b1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a - 4\) , \( -4 a - 13\bigr] \)
324.3-b2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 106 a + 341\) , \( 251 a + 791\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph