Elliptic curve isogeny class 81.4-a over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-81.4-a
• Conductor: 81.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 81.4-a over \(\Q(\sqrt{13}) \)

Isogeny class 81.4-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
81.4-a1	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -7 a + 12\) , \( -16 a + 34\bigr] \)
81.4-a2	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 2 a + 2\) , \( a + 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph