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

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-196.1-f
• 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-f over \(\Q(\sqrt{37}) \)

Isogeny class 196.1-f contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
196.1-f1	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -6 a - 47\) , \( a + 85\bigr] \)
196.1-f2	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -246 a - 657\) , \( 3053 a + 7841\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph