Elliptic curve isogeny class 1.1-a over number field \(\Q(\sqrt{37}) \)

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-1.1-a
• Conductor: 1.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1.1-a over \(\Q(\sqrt{37}) \)

Isogeny class 1.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
1.1-a1	\( \bigl[0\) , \( -1\) , \( 1\) , \( 8 a - 28\) , \( -19 a + 67\bigr] \)
1.1-a2	\( \bigl[0\) , \( -1\) , \( 1\) , \( 1688 a - 5978\) , \( 65277 a - 231171\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph