Elliptic curve isogeny class 729.1-e over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-729.1-e
• Conductor: 729.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 729.1-e over \(\Q(\sqrt{13}) \)

Isogeny class 729.1-e contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
729.1-e1	\( \bigl[a\) , \( -a\) , \( 1\) , \( a - 6\) , \( 6 a - 15\bigr] \)
729.1-e2	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -8 a + 16\) , \( -17 a + 37\bigr] \)