Elliptic curve isogeny class 324.5-f over number field \(\Q(\sqrt{37}) \)

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-324.5-f
• Conductor: 324.5
• Rank: \( 1 \)

Base field \(\Q(\sqrt{37}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 9 \); class number \(1\).

Elliptic curves in class 324.5-f over \(\Q(\sqrt{37}) \)

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

Curve label	Weierstrass Coefficients
324.5-f1	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -3 a - 7\) , \( a + 1\bigr] \)
324.5-f2	\( \bigl[1\) , \( -a\) , \( 0\) , \( -21 a + 78\) , \( -117 a + 413\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph