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

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-576.1-e
• Conductor: 576.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

Isogeny class 576.1-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
576.1-e1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -1040 a - 2648\) , \( -45856 a - 116544\bigr] \)
576.1-e2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 225 a + 572\) , \( -3033 a - 7708\bigr] \)
576.1-e3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -80 a - 203\) , \( -484 a - 1230\bigr] \)
576.1-e4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -225 a + 797\) , \( 3033 a - 10741\bigr] \)
576.1-e5	\( \bigl[0\) , \( 1\) , \( 0\) , \( -1160 a - 2948\) , \( -37888 a - 96288\bigr] \)
576.1-e6	\( \bigl[0\) , \( 1\) , \( 0\) , \( 1040 a - 3688\) , \( 45856 a - 162400\bigr] \)