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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-300.3-i
• 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-i over \(\Q(\sqrt{21}) \)

Isogeny class 300.3-i contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
300.3-i1	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -5 a + 7\) , \( -9 a + 21\bigr] \)
300.3-i2	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 645 a - 1983\) , \( -13939 a + 39701\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph