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

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

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

Isogeny class 441.9-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
441.9-d1	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 80 a - 277\) , \( -694 a + 2458\bigr] \)
441.9-d2	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 33 a + 83\) , \( 1128 a + 2866\bigr] \)
441.9-d3	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -692 a - 1757\) , \( 14400 a + 36592\bigr] \)
441.9-d4	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 15 a - 77\) , \( -1666 a + 5788\bigr] \)