Elliptic curve isogeny class 324.1-r over number field \(\Q(\sqrt{37}) \)

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-324.1-r
• Conductor: 324.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 324.1-r over \(\Q(\sqrt{37}) \)

Isogeny class 324.1-r contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
324.1-r1	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( a - 2\) , \( 115 a + 298\bigr] \)
324.1-r2	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -179 a - 542\) , \( 2491 a + 6670\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph