Elliptic curve isogeny class 324.5-b over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-324.5-b
• Conductor: 324.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 324.5-b over \(\Q(\sqrt{13}) \)

Isogeny class 324.5-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
324.5-b1	\( \bigl[a\) , \( 0\) , \( 1\) , \( 2 a - 6\) , \( -14 a + 32\bigr] \)
324.5-b2	\( \bigl[a\) , \( 0\) , \( 1\) , \( -23 a + 54\) , \( 370 a - 850\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph