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

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

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

Curve label	Weierstrass Coefficients
196.1-d1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 907 a - 3788\) , \( 29235 a - 109976\bigr] \)
196.1-d2	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 17 a - 58\) , \( 11 a - 54\bigr] \)
196.1-d3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 12 a - 33\) , \( -29 a + 109\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph