Elliptic curve isogeny class 576.1-m over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-576.1-m
• Conductor: 576.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{21}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 5 \); class number \(1\).

Elliptic curves in class 576.1-m over \(\Q(\sqrt{21}) \)

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

Curve label	Weierstrass Coefficients
576.1-m1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 1\) , \( -2 a - 3\bigr] \)
576.1-m2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -14 a - 89\) , \( 49 a - 93\bigr] \)
576.1-m3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -14 a - 29\) , \( -71 a - 129\bigr] \)
576.1-m4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -254 a - 449\) , \( -3647 a - 6549\bigr] \)

Rank

Rank: \( 0 \)

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