Elliptic curve isogeny class 324.4-e over number field \(\Q(\sqrt{37}) \)

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-324.4-e
• Conductor: 324.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 324.4-e over \(\Q(\sqrt{37}) \)

Isogeny class 324.4-e contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
324.4-e1	\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -6 a - 2\) , \( 5 a + 1\bigr] \)
324.4-e2	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 216 a - 767\) , \( 2969 a - 10520\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph