Elliptic curve isogeny class 676.1-a over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-676.1-a
• Conductor: 676.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 676.1-a over \(\Q(\sqrt{21}) \)

Isogeny class 676.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
676.1-a1	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 2297 a - 6434\) , \( -89617 a + 250159\bigr] \)
676.1-a2	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 22 a - 64\) , \( -164 a + 455\bigr] \)
676.1-a3	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -3 a + 6\) , \( 3 a - 11\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph