Elliptic curve isogeny class 9.3-a over number field \(\Q(\sqrt{37}) \)

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-9.3-a
• Conductor: 9.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 9.3-a over \(\Q(\sqrt{37}) \)

Isogeny class 9.3-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
9.3-a1	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 2 a - 5\) , \( -5 a + 18\bigr] \)
9.3-a2	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 492 a - 1755\) , \( 9865 a - 34926\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph