Elliptic curve isogeny class 300.2-l over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-300.2-l
• Conductor: 300.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 300.2-l over \(\Q(\sqrt{21}) \)

Isogeny class 300.2-l contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
300.2-l1	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 855 a - 2519\) , \( 20702 a - 58643\bigr] \)
300.2-l2	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 5 a - 9\) , \( -8 a + 27\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph