Elliptic curve isogeny class 441.3-e over number field \(\Q(\sqrt{37}) \)

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-441.3-e
• Conductor: 441.3
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 441.3-e over \(\Q(\sqrt{37}) \)

Isogeny class 441.3-e contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
441.3-e1	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 2 a - 1\) , \( a - 1\bigr] \)
441.3-e2	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -33 a - 56\) , \( 93 a + 213\bigr] \)