Elliptic curve isogeny class 900.2-p over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-900.2-p
• Conductor: 900.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 900.2-p over \(\Q(\sqrt{21}) \)

Isogeny class 900.2-p contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
900.2-p1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -833 a - 1340\) , \( -18677 a - 40710\bigr] \)
900.2-p2	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -38 a - 365\) , \( 1057 a - 15\bigr] \)