Elliptic curve isogeny class 729.2-g over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-729.2-g
• Conductor: 729.2
• 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 729.2-g over \(\Q(\sqrt{13}) \)

Isogeny class 729.2-g contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
729.2-g1	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -4 a - 3\) , \( 2 a + 6\bigr] \)
729.2-g2	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 5 a + 3\) , \( 2 a + 6\bigr] \)