Elliptic curve isogeny class 100.2-d over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-100.2-d
• Conductor: 100.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 100.2-d over \(\Q(\sqrt{21}) \)

Isogeny class 100.2-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
100.2-d1	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 4 a + 7\) , \( -40 a - 72\bigr] \)
100.2-d2	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -76 a - 143\) , \( -464 a - 842\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph