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

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-324.5-e
• 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-e over \(\Q(\sqrt{37}) \)

Isogeny class 324.5-e contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
324.5-e1	\( \bigl[1\) , \( -1\) , \( a\) , \( -217 a - 550\) , \( -2970 a - 7550\bigr] \)
324.5-e2	\( \bigl[a\) , \( -a\) , \( 1\) , \( 5 a - 7\) , \( -5 a + 6\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph