Elliptic curve isogeny class 196.1-g over number field \(\Q(\sqrt{37}) \)

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-196.1-g
• Conductor: 196.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 196.1-g over \(\Q(\sqrt{37}) \)

Isogeny class 196.1-g contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
196.1-g1	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -17 a - 41\) , \( -11 a - 43\bigr] \)
196.1-g2	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -12 a - 21\) , \( 29 a + 80\bigr] \)
196.1-g3	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -907 a - 2881\) , \( -29235 a - 80741\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)

Isogeny graph