Elliptic curve isogeny class 1521.3-b over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1521.3-b
• Conductor: 1521.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 1521.3-b over \(\Q(\sqrt{13}) \)

Isogeny class 1521.3-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
1521.3-b1	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 17 a - 81\) , \( -74 a + 263\bigr] \)
1521.3-b2	\( \bigl[1\) , \( -a\) , \( 0\) , \( 24 a + 30\) , \( -27 a - 31\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph