Elliptic curve isogeny class 81.3-a over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-81.3-a
• Conductor: 81.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 81.3-a over \(\Q(\sqrt{13}) \)

Isogeny class 81.3-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
81.3-a1	\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -2 a + 2\) , \( -2 a + 1\bigr] \)
81.3-a2	\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -2 a - 1\) , \( -11 a - 14\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph