Elliptic curve isogeny class 441.9-f over number field \(\Q(\sqrt{37}) \)

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-441.9-f
• Conductor: 441.9
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 441.9-f over \(\Q(\sqrt{37}) \)

Isogeny class 441.9-f contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
441.9-f1	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -176 a - 530\) , \( -2689 a - 7103\bigr] \)
441.9-f2	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -3021 a - 7720\) , \( -162246 a - 412881\bigr] \)