Elliptic curve isogeny class 17.1-a over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-17.1-a
• Conductor: 17.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 17.1-a over \(\Q(\sqrt{21}) \)

Isogeny class 17.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
17.1-a1	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -7\) , \( -2 a + 2\bigr] \)
17.1-a2	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -15 a + 33\) , \( 10 a - 33\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph