Elliptic curve isogeny class 147.1-e over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-147.1-e
• Conductor: 147.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 147.1-e over \(\Q(\sqrt{21}) \)

Isogeny class 147.1-e contains 2 curves linked by isogenies of degree 13.

Curve label	Weierstrass Coefficients
147.1-e1	\( \bigl[0\) , \( -a\) , \( 1\) , \( 4562 a - 12771\) , \( 257501 a - 718820\bigr] \)
147.1-e2	\( \bigl[0\) , \( -a\) , \( 1\) , \( 12 a - 31\) , \( -29 a + 80\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph