Elliptic curve isogeny class 300.3-a over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-300.3-a
• Conductor: 300.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 300.3-a over \(\Q(\sqrt{21}) \)

Isogeny class 300.3-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
300.3-a1	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -2 a + 2\) , \( 22 a - 62\bigr] \)
300.3-a2	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 58 a - 198\) , \( 482 a - 1262\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph