Elliptic curve isogeny class 637.1-b over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-637.1-b
• Conductor: 637.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 637.1-b over \(\Q(\sqrt{13}) \)

Isogeny class 637.1-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
637.1-b1	\( \bigl[0\) , \( 1\) , \( 1\) , \( -7\) , \( 5\bigr] \)
637.1-b2	\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \)
637.1-b3	\( \bigl[0\) , \( 1\) , \( 1\) , \( 13\) , \( 42\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph