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

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1521.3-k
• Conductor: 1521.3
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
1521.3-k1	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -3 a - 19\) , \( -17 a - 6\bigr] \)
1521.3-k2	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -98 a - 134\) , \( -744 a - 923\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph