Elliptic curve isogeny class 2268.1-q over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-2268.1-q
• Conductor: 2268.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 2268.1-q over \(\Q(\sqrt{21}) \)

Isogeny class 2268.1-q contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
2268.1-q1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -516 a - 912\) , \( -9450 a - 16952\bigr] \)
2268.1-q2	\( \bigl[1\) , \( -1\) , \( 0\) , \( -6 a - 12\) , \( -12 a - 20\bigr] \)
2268.1-q3	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 61 a + 109\) , \( -192 a - 344\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph