Elliptic curve isogeny class 100.3-d over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-100.3-d
• Conductor: 100.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 100.3-d over \(\Q(\sqrt{21}) \)

Isogeny class 100.3-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
100.3-d1	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -4 a + 16\) , \( 35 a - 95\bigr] \)
100.3-d2	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 76 a - 214\) , \( 539 a - 1519\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph