Elliptic curve isogeny class 324.3-d over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-324.3-d
• Conductor: 324.3
• Rank: \( 1 \)

Base field \(\Q(\sqrt{13}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 3 \); class number \(1\).

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 324.3-d over \(\Q(\sqrt{13}) \)

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

Curve label	Weierstrass Coefficients
324.3-d1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 5 a - 2\) , \( -3 a + 12\bigr] \)
324.3-d2	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 11 a - 14\) , \( -15 a + 39\bigr] \)