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

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-324.1-u
• 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-u over \(\Q(\sqrt{37}) \)

Isogeny class 324.1-u contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
324.1-u1	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -110 a + 94\) , \( -238 a - 1024\bigr] \)
324.1-u2	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 10 a - 41\) , \( 33 a - 124\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph