Elliptic curve isogeny class 700.1-c over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-700.1-c
• Conductor: 700.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 700.1-c over \(\Q(\sqrt{21}) \)

Isogeny class 700.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
700.1-c1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 2\) , \( -3\bigr] \)
700.1-c2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -18\) , \( -19\bigr] \)
700.1-c3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -88\) , \( 317\bigr] \)
700.1-c4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -268\) , \( -1619\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph