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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-576.1-g
• 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-g over \(\Q(\sqrt{21}) \)

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

Curve label	Weierstrass Coefficients
576.1-g1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 54 a - 249\) , \( -495 a + 1647\bigr] \)
576.1-g2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -21 a - 39\) , \( 36 a + 171\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph