Elliptic curve isogeny class 1764.1-l over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1764.1-l
• Conductor: 1764.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1764.1-l over \(\Q(\sqrt{21}) \)

Isogeny class 1764.1-l contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
1764.1-l1	\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 188 a - 526\) , \( 9119 a - 25496\bigr] \)
1764.1-l2	\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 5228 a - 14806\) , \( 313199 a - 876080\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph