Elliptic curve isogeny class 1296.1-a over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1296.1-a
• Conductor: 1296.1
• 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 1296.1-a over \(\Q(\sqrt{21}) \)

Isogeny class 1296.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
1296.1-a1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -765 a - 1386\) , \( -17544 a - 31458\bigr] \)
1296.1-a2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 765 a - 2151\) , \( 17544 a - 49002\bigr] \)