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

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-576.1-u
• 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-u over \(\Q(\sqrt{37}) \)

Isogeny class 576.1-u contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
576.1-u1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4 a + 8\) , \( -16 a - 44\bigr] \)
576.1-u2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6 a - 17\) , \( 27 a + 69\bigr] \)
576.1-u3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -a - 2\) , \( 0\bigr] \)
576.1-u4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -31 a - 77\) , \( -123 a - 312\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph