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

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-441.9-e
• 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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

Isogeny class 441.9-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
441.9-e1	\( \bigl[a\) , \( -a\) , \( 1\) , \( 51 a - 182\) , \( 341 a - 1208\bigr] \)
441.9-e2	\( \bigl[a\) , \( -a\) , \( 1\) , \( 776 a - 2752\) , \( 21667 a - 76732\bigr] \)
441.9-e3	\( \bigl[a\) , \( -a\) , \( 1\) , \( 12441 a - 44072\) , \( 1335073 a - 4727986\bigr] \)
441.9-e4	\( \bigl[a\) , \( -a\) , \( 1\) , \( 711 a - 2552\) , \( 24885 a - 88194\bigr] \)