Elliptic curve isogeny class 9.2-a over number field \(\Q(\sqrt{37}) \)

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-9.2-a
• Conductor: 9.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 9.2-a over \(\Q(\sqrt{37}) \)

Isogeny class 9.2-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
9.2-a1	\( \bigl[0\) , \( -a\) , \( 1\) , \( -2 a - 3\) , \( 5 a + 13\bigr] \)
9.2-a2	\( \bigl[0\) , \( -a\) , \( 1\) , \( -492 a - 1263\) , \( -9865 a - 25061\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph