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

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-81.3-b
• 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-b over \(\Q(\sqrt{13}) \)

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

Curve label	Weierstrass Coefficients
81.3-b1	\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( -6 a + 9\) , \( 4 a - 19\bigr] \)
81.3-b2	\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( -3 a - 3\) , \( -26 a - 34\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph