Elliptic curve isogeny class 52.1-a over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-52.1-a
• Conductor: 52.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 52.1-a over \(\Q(\sqrt{13}) \)

Isogeny class 52.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
52.1-a1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -460\) , \( -3830\bigr] \)
52.1-a2	\( \bigl[1\) , \( 0\) , \( 1\) , \( -5\) , \( -8\bigr] \)
52.1-a3	\( \bigl[1\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph