Elliptic curve isogeny class 576.1-x over number field \(\Q(\sqrt{37}) \)

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-576.1-x
• Conductor: 576.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 576.1-x over \(\Q(\sqrt{37}) \)

Isogeny class 576.1-x contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
576.1-x1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a - 13\) , \( 4 a + 5\bigr] \)
576.1-x2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -67 a - 193\) , \( 463 a + 1220\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph