Elliptic curve isogeny class 729.3-g over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-729.3-g
• Conductor: 729.3
• 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 729.3-g over \(\Q(\sqrt{13}) \)

Isogeny class 729.3-g contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
729.3-g1	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -7 a + 9\) , \( -3 a + 8\bigr] \)
729.3-g2	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 2 a - 6\) , \( -3 a + 9\bigr] \)